







The equation of a line 
20180123 

From Gloria: Write the equation of a line in standard form through the point (1, 6) and perpendicular to the line 2x –y = 9. Answered by Penny Nom. 





What is the grade of the incline? 
20170312 

From Jon: If I am climbing 16 feet in elevation over 80 feet horizontal. What is the grade of the incline Answered by Penny Nom. 





The equation of a ski slope 
20160831 

From Hannah: The information provided is
A ski slope has a slope of 0.2. You start at an altitude of 10,000ft.
Then the question is "Write the equation giving altitude (a) as a function of horizontal distance moved (d).
I know this is probably a very simple question but I didn't take a math class my senior year and now I'm a freshman in college, so some of it is very frustrating to me.
Any help is much appreciated, thank you! Answered by Penny Nom. 





Slope 
20160627 

From Ashiq: What is 1% slope if length 101 feet? Answered by Penny Nom. 





Sloping my yard away from my house 
20160415 

From Harold: I need to slope a area of my yard away from my house and garage. The length of my house is 80 feet long and i need to slope it 22 feet away. I want to raise the dirt at the foundation by 6 inches and slope it down to nothing at the width of 22 feet. How much soil would i require? Answered by Penny Nom. 





A pipe is installed with a 2% grade 
20160107 

From peter: a sewer ditches to be 148 feet long. the pipe is installed with a 2% grade.
what would be total amount of fall be? Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





A question concerning two lines 
20140509 

From Hela: The equation of the line L is 6x+5y=3, and the equation of line Q is 5x6y=0, which statement below about the line is true?
A) same y intercept
B)parallel
C) Same x intercept
D)perpendicular Answered by Penny Nom. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





Gradient 
20140221 

From Nancy: calculate the gradient of the line AB when the line AB is passing through the points A (2,1,) and B ( 4, 3).) Answered by Penny Nom. 





The grade of a road as a percent 
20140214 

From Emily: What is the grade of the road shown below expressed as a percent rounded to one decimal place?
Rise is 40feet
Run is 380 feet Answered by Penny Nom. 





The slope of the line y=2x+5 
20131229 

From victoria: what is the slope of the line with the equation y=2x+5 Answered by Penny Nom. 





What is the slope of this line? 
20131201 

From Charlene: What is the slope of this line? Answered by Penny Nom. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





Slope 
20120516 

From Kodie: What is the easiest way to find slope? Answered by Penny Nom. 





A sloped yard 
20120424 

From William: Trying to calculate fill dirt for leveling a sloped yard to place a slab. Slab is 30'x40', yard slopes from corner #1 south 40' to Corner #4 drop is 11". From corner #1 east 30' to corner #2, drop is 11 1/4". From corner #1 southeast at a 45 degrees, 50' to corner #3, drop is 19 3/4". Corners numbered in a clockwise direction. Answered by Penny Nom. 





An equation of the form y=mx 
20120417 

From Samiya: what would be an equation of the form y=mx with the points (2, 6) and (1, 3) for the line? Answered by Penny Nom. 





The slope of a line 
20111110 

From Sara: Line k lies in the xyplane.
The xintercept of line k is 4.
And line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0).
What is the slope of line k?
Give the answer as a fraction. Answered by Penny Nom. 





A column and a sloped ceiling 
20110610 

From Tom: Hi! I am a woodworker who needs some help finding a formula. I have to make a cylinder shape column that butts up against a sloped ceiling using bending plywood. I need to figure out how to cut the shape on this flat piece of material. The diameter of the column is 54.375". The tallest point is 9 13/16" and the shortest point is 4 7/16". Any help would be greatly appreciated. Answered by Harley Weston. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





The slope of a hole 
20101028 

From William: What is the slope of a hole that is 7.4 mm in dia by .5mm in depth. Answered by Penny Nom. 





The equation of a line 
20101019 

From Sava: I have to write an equation and sketch a graph for the line that meets the given conditions:
A line with slope 15/5 that passes through the point (2.5,4.5) Answered by Penny Nom. 





The rate of change of y with respect to x 
20100429 

From Tom: I just had a quick calc question about wording that wasn't ever
addressed in class. When the book says "the rate of change of y with
respect to x", should it be considered how fast y is changing in
comparison to x?
I ask because the textbook says that "y is changing 3 times faster than x,
so the rate of change of y with respect to x is 3." I'm use to rate being
like velocity, as in units of distance per units of time. All we're told
in class is that it's the slope of the tangent line, I was hoping you
could clarify for me what exactly is meant by the wording of a "rate of
change of something with respect to something else". More specifically, what
"rate" and "with respect to" mean within this context?
Thanks for your time Answered by Harley Weston. 





One in twenty as a percentage 
20100427 

From jim: Please advise how I work out a gradient of say 120 one in twenty as a percentage % Answered by Penny Nom. 





Modelling the roof of a house 
20100323 

From Sandi: This question has been haunting my dreams at night. It states the cross section of the roof of a house is modelled by the function y= 5\12x12+5, where y>0 or y. Now I'm suppose to graph the function. b) Find the slope, height, length of sides, and base of the isosceles triangle. c)Explain what transformation must be applied to the graph of y=x to obtain the graph of y= 5\12x12+5, where y>0 or y=0. 1st I put the equation into my calculator and graphed it. I got 10 for the height. We have had 2 sub teachers this past week. The first one told me the height should be 12 the other one told me 5. So I'm really confused. If I use my 10 units as height and the Pythagorean Theorem I get my sides to be 26 units the base 48 and my slope I calc to be 5/12. Both teachers are pretty sure I'm wrong and they are right but we all have different answers. Please help put this problem to rest so I can rest soundly at night. Thank you for your time. Answered by Penny Nom. 





The line joining (3,4) and (5,6) 
20100306 

From Patric: Find the condition that the point (x,y) may lie on the line joining the points
(3,4) and (5,6) Answered by Penny Nom. 





Is it a rectangle? 
20091029 

From sefora: The coordinates of the vertices of quadrilaterals are given.
Draw each quadrilateral on a grid.
Determine whether it is a rectangle (show your work)
P(5,1), Q(4,4), R(6,2), S(3,5) Answered by Penny Nom. 





A linear equation 
20091022 

From Ryan: How do you convert the equation 2x6y=7? This is on my homework and I am really stuck!!! Answered by Penny Nom. 





The slopeintercept form 
20090911 

From Shelby: Write an equation in slopeintercept form of the line that is parallel to the graph of 3y4x=1 and passes through (0,6) Answered by Penny Nom. 





Parallel lines 
20090701 

From chris: Write the slope of a line that is parallel to each line.
1.y=2x5
2.y=x+2
3.3x+y=10
4.5xy=11
5.x+2y=6
6.2x3y=9
7.4x+y=3
8.x+2y=14 Answered by Brennan Yaremko. 





The product of gradients between 2 perpendiculars lines 
20090611 

From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to 1.... Answered by Penny Nom. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





A slopped table top 
20090316 

From anthony: A perfect circle with radius 100m is supported by four legs, 50m long. The circle is flat when all four legs are 50m long, and tilted when the legs are different in length. The four legs are spread evenly 90 degrees apart at 0, 90, 180, and 270. Find the high and low points in degree and height when the legs are 55m at 0 degree, 70m at 90 degree, 45m at 180 degree, and 30m at 270 degree.
Not sure if they can be calculated using only 2 or 3 legs.
I have tried by picking the two adjacent highest legs (55m and 70m) so I know the high point falls into the first quadrant. Then I tried using ratio to determine where the high point is, which I think high point should be closer to the 70m leg, I am not sure. If I can find the high point, the low point should be opposite to it. Answered by Chris Fisher and Harley Weston. 





The slope of a line 
20090309 

From Shannon: Find x such that a straight line passing through (2,x) and (x+1, 3) has slope 2x+1/x1
Please help! Missed this class, so I have no notes and the book doesn't have an example like this.
Thank you! Answered by Penny Nom. 





A line parallel to a given line 
20090218 

From Lisa: I'm having a hard time understanding the concept of how to write an
equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y=mx+b.
(7,9); 2x+5y=4. i would appreciate it alot if someone can show ne how
to do this. Thank you, Lisa Answered by Penny Nom. 





Grade of a hill 
20090126 

From rachel: if the grade is 18%, how many feet would it fall vertically over a horizontal distance of 250 yards. Answered by Robert Dawson. 





A line is perpendicular to another line 
20090116 

From Greg: A line is perpendicular to the line y=2x+3 and has the same xintercept as x+3y+10.
Find the equation of this line. Express your answer in the form of y=mx+b. Justify your answer. Answered by Robert Dawson. 





The slope intercept form 
20090111 

From Norma: write equation in slope intercept form and then find the slope and yintercpet of the corresponding line.
please show step by step
1). 2x3y9=0 and 2). 3x4y+8=0 Answered by Penny Nom. 





A line in slope intercept form 
20081208 

From laurie: the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3 Answered by Penny Nom. 





The sides of a rectangle 
20081208 

From Mitchell: The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y60=0
Point C is at (18, 14).
What is the length of segment AD? Answered by Penny Nom. 





The slope of a tangent line 
20081018 

From Amanda: If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Answered by Stephen La Rocque. 





A tangent line to f(x) = 1/(x  1) 
20081016 

From Amanda: If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Answered by Harley Weston. 





Perpendicular lines 
20081016 

From Hailey: In the xyplane,
the line with equation 2x + y = 3
is perpendicular to the line with equation y = mx + b,
where m and b are constants.
What is the value of m? Answered by Penny Nom. 





The rise over the run 
20081007 

From Mak: what is the ratio of the rise to run? Answered by Penny Nom. 





The standard form Ax+By=C 
20080926 

From Susan: I am having difficulty changing the pointslope form of the equation of the line yy1=m(xx1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way. Answered by Penny Nom. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





Parallel and perpendicular lines 
20080906 

From C: Can you help me determine whether these lines are parallel, perpendicular or neither and why?
Problem 1: y=3x+2
y=1/3x  4
Problem 2: y=1/3x + 1/2
y=1/3 x 2 Answered by Penny Nom. 





Slope and rate of change 
20080623 

From Lee: What is the difference between a slope and a rate of change? Answered by Stephen La Rocque. 





A jar of pennies 
20080618 

From Ryan: if you are given a jar of pennies and you had to find the weight of one penny
without opening the jar.when you graph it, You have to y= the mass of the container and x= number of coins
you use the slope to find the weight of the penny how would u go about doing that? Answered by Stephen La Rocque. 





What is a 1% slope? 
20080617 

From randy: trying to figure out percentage of slope lets say i have to run a pipe 80' at a 1%slope how much pitch is that? Answered by Harley Weston. 





Elevation gain 
20080518 

From Mark: How do you calculate elevation gain on a treadmill? e.g. 5.0 miles (26,400ft) @ 15% incline.
I have been estimating it as 26,400 x .15 = 3,960 ft of elevation gain.
Hopeful Mount Rainier Climber Answered by Victoria West. 





The slope intercept form 
20080411 

From Dave: Hi, why is there a yintercept in the slope intercept form?What does the yintecept have to do with the equation? Answered by Penny Nom. 





The equation of a line 
20080217 

From Jennifer: Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form ) Answered by Penny Nom. 





The slope intercept form of a line 
20080217 

From chris: find the slope and y intercept of the line (2x+4)3y=11(x1)
is this equation in slope point form. Answered by Penny Nom. 





Find the slope of the line with equation 73y=2x 
20080123 

From nell: Find the slope of the line with equation 73y=2x Answered by Stephen La Rocque. 





The equation of a line 
20080120 

From Sara: The question is:
Write the equation of a line that is parallel to y=3x2 through the point (5,9).
I think the correct equation for this is y=3x+24.
But I have to write it in standard form, and I can't seem to figure out how to do that. Please answer soon! Thanks! Answered by Stephen La Rocque and Penny Nom. 





The line through (22 ;1) and (23, 2) 
20080120 

From Zachery: i have a slope that equals 1/1 and my coordinates are (22;1) and (23;2) and i am trying to change it into the equation y=mx+b and the farthest that i've gotten is y=1x_ (i can not find out how to find b.) So i was wondering if you could help me find out what b is because i have got no clue!!!!! Answered by Penny Nom. 





Why do they use the letter b in y=mx+b? 
20071115 

From virginia: why do they use the letter b in y=mx+b?
im asking this because my math teacher said he will give extra points to anyone who finds this out first
and i was hoping you guys would be the ones who could help. Answered by Penny Nom. 





Roof trusses 
20071005 

From Mary: I need to know how algebra is used in making or designing of roof trusses for a house. I have to present a poster in class showing how algebra is used in daily jobs. My dad works at a truss company. Answered by Chris Langdon. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Equation of a tangent line to a function 
20071004 

From Princess: If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Answered by Stephen La Rocque. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





The incline of my yard as it slopes away from my house 
20070922 

From Janet: I need to calculate the degree (or is it percent?) of incline of my yard as it
slopes away from my house. Do I visualize a right angle formed by a
level line from the bottom of the slope to the side of the house, and then
compare the line of the slope against the right angle to get the degree?
Or is an incline calculated by the measurement of the rise in 100 feet? For
instance, if the ground rises 3 feel in a distance of 100 feet, is that a 3%
incline? And if it rises 4 feet in a distance of 25 feet, is that a 16% incline?
Thanks so much. Answered by Stephen La Rocque. 





The slope of a line 
20070906 

From Danielle: Hello. I need some help with this: i am supposed to find the equation of a line with a point
(2/3,5) and (5/6,4) the answer in the book says y=6x+1. My question is how did they get
for the slope? Answered by Penny Nom. 





Perpendicular lines 
20070906 

From dinesh: we know that for two perpendicular lines
m1*m2=1perpendicular
but this is not true for xaxis and yaxis? Answered by Harley Weston. 





Pointslope form 
20070816 

From jenny: write an equation in the pointslope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,1)
slope= 5,passing through (4,2)
slope= 2,passing through(0,3) Answered by Leeanne Boehm. 





Slopes of a triangle's medians 
20070811 

From Gina: I am trying to help my daughter with this, but I am very weak in Math.Please help!
Find slopes of the medians of a triangle whose vertices are P(1,3), Q(3,5), and R(6,2) Answered by Stephen La Rocque. 





Dirt in a sloped round hole 
20070803 

From Ken: How much dirt do I need to fill a ground hole 20 ft in dia. with a sloping floor that has a ht. of 5" on one side and 12" on the other side? Answered by Stephen La Rocque. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Road incline grades 
20070507 

From cecil: convert grade percent to degrees Answered by Stephen La Rocque. 





Finding out if two line equations are parallel or perpendicular 
20070428 

From Vincent: Can you determine if the two lines are parallel, perpendicular, or neither
1/2x+4y=3/5
y/1 + 10/5= 8x
I think there perpendicular but how would you solve the equations Answered by Stephen La Rocque. 





The grade of a shoulder 
20070428 

From Robert: I am building a road with a 1.2 meter shoulder. The plan calls fo a 6% shoulder grade. When I use my metric calculator I come up with a different answer when I multiply 3/4 of an inch by 1.2 meters and when I multiply 1.2 meters by .06%? Answered by Penny Nom. 





The angles in a right triangle 
20070328 

From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom. 





Slopes of perpendicular lines 
20070327 

From Mykolyn: How do you find the slope of a line that is perpendicular to the graph of:
y= 1/2x+4? Answered by Leeanne Boehm and Sara Ulmer. 





yintercept form 
20070316 

From Ken: Simple way on how to convert to & from yintercept form & Std. form.
Eg: Convert into yintercept form: 3x+4y+7=0,
Eg.: Convert into Std. Form: y=1/2x +3, y=50x +300. I would appreciate your
help in this matter, as I find it hard to understand.
Kind Regards: Ken Answered by Penny Nom. 





Slope 
20070302 

From Lacey: My algebra 2 class is researching graphing and slope and we would like to know how we use graphing and slope in everyday life. So if you could get back to me with some real world examples i would really appreciate it. Thanks for your help! Answered by Steve La Rocque, Penny Nom and Sara Ulmer. 





Percent elevation gain 
20070124 

From Susan: okay... so if I hike Gregory Canyon and it's a 1.1 mile hike with a 900 foot elevation gain, what's the percent elevation gain? Answered by Stephen La Rocque. 





A line perpendicular to another line 
20070113 

From Dusty: Find an equation for the line perpendicular to: 3x  4y + 1 = 0 passing through (4,7) Answered by Leeanne Boehm and Penny Nom. 





The slopeintercept form 
20070104 

From Earnestine: Given a line containing the points (1,4), (2,7), and (3,10) determine the slopeintercept form of the equation, provide one additional point on this line, and graph the function. Answered by Penny Nom. 





The slopeintercept form 
20061217 

From Anthony: I'm really confused with this, tried to figure it out on my own but i can't seem to grasp it here's the problem: Two points are given a. Write an equation in slopeintercept form for the line containing the two points. b. Graph the line from Part a and check that both points are on the line. Answered by Penny Nom. 





Th pitch of a roof 
20061215 

From Rob: I am trying to determine how much to add for roof pitch. I guess the best way would be to use a right triangle as an example.
The base of the triangle is always 12 inches. The leg pointing straight up is a variable. I will say 6" in this example. By changing the variable how can i determine how much longer the hypotenuse than the base expressed in percent or decimal. Answered by Stephen La Rocque. 





The grade of a highway 
20061114 

From Nancy: If a portion of highway has a grade or slope of 12%, and the length of this portion is approximately 1.1 miles, what is the change in elevation from the top of the grade to the bottom of the grade in feet? Answered by Stephen La Rocque and Penny Nom. 





The slopeintercept form 
20061108 

From Kilihea: I need to graph this equation but first need to turn it into a slopeintercept form. 6x  3y = 3 I would really appreciate it if you could help me turn it into a slopeintercept form. Answered by Penny Nom. 





Convert a standard form to a slope intercept form 
20060914 

From Maiko: I need to know step by step procedures to convert a standard form to a slope intercept form? Answered by Penny Nom. 





How old is y = mx + b? 
20060705 

From Beckie: I am taking intermediate algebra this summer (Math 95), and have a question for you. My instructor will award extra credit points to any of us who find out how old the formula
y = mx+b is. Would you happen to know the answer? Answered by Penny Nom. 





Equation of a line in Ax + By = C form 
20060419 

From Christopher: How do you write the equation of a line with a slope of 3/8 and passing through (4,6) in Ax+By=C form? Answered by Stephen La Rocque. 





Intercepts and slope 
20060115 

From Anthony: Given 1.7x + 0.8y=7.1:
(a) state the intercepts and slope for the graph
(b) Draw the graph Answered by Penny Nom. 





y  y1 = m(x  x1) 
20060108 

From Greg: How do you change 2x + 3y = 7 into y  y1 = m(xx1)?
Answered by Penny Nom. 





A tangent to a parabola 
20051102 

From A student: Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Answered by Penny Nom. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





Two intersecting lines 
20041218 

From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston. 





The point slope form of a line 
20041026 

From Jack: Given a set of ordered pairs, ie (1,1) (2,4) (3,7), how does one determine the rule f(n) other than by trial and error Answered by Penny Nom. 





The equation of a line 
20040430 

From Amy: Write the equation of the line that contains the point (4,6) and is perpendicular to the line y=5x+100. Answered by Penny Nom. 





The line through (4,2) and (4,8) 
20040417 

From Kim: Write an equation for the line.
Given points (4, 8) and (4,2) are on the line.
I believe m=undefined.
How do I solve for b when m is undefined, and then plug in the values for m, b, and y?
Answered by Penny Nom. 





The incline of an exercise machine 
20040202 

From An exerciser: This is a question about incline percentage. On an exercise machine if the elevation is raised 3 and one half inches from a level position then what would be the incline percentage? Answered by Penny Nom. 





The slope of a tangent 
20031001 

From A student:
find the slope of the tangent to each curve at the given point f(x)=square root 16x, where y=5 Answered by Penny Nom. 





The incline of a road 
20030803 

From A driver: incline % grade as to degree. ie 6% hwy grade= what degree of incline? Answered by Penny Nom. 





Slope 
20030720 

From Brian:
You are placing a pipe 60 feet long at a slope of 1.5%. How would you figure the amount of drop from the inlet of the pipe tot he outlet of the pipe? and what is the answer . If you are trying to keep a shoulder slope of a road between 3/4'' per foot and 11/2'' per foot . If the shoulder is 10 feet wide, how would you figure how much lower should the outside of the shoulder be than the edge of pavement and what is the answer ? Answered by Penny Nom. 





A tangent to a circle 
20030418 

From Lech: The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Answered by Harley Weston. 





The percentage grade of that hill 
20021105 

From Cathy: If there is an 80ft climb over a kilometer(about 3280ft) what is the percentage grade of that hill? Answered by Penny Nom. 





6% grade 
20021015 

From Micheal: When I am driving down the road and see a sign that says for example steep grade ahead 6% grade etc etc what does this mean? Answered by Penny Nom. 





A linear function 
20020909 

From Chad: If y = 9x  13 does it represent a linear function? And if it does what is its slope and is it a direct variation? Answered by Peny Nom. 





The slope of a tangent line 
20020304 

From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston. 





The slopes of the sides of the Great Pyramid 
20020209 

From Christina: The Great Pyramid is the largest of the Egyptian pryamids. When it was built, it was 481 feet tall and had a square base with 755foot sides. The pyramid has two different slopesone along its sides and the other along its edges. Which slope is steeper? Answered by Penny Nom. 





Slope intercept form 
20011127 

From A student: what is slope intercept form? Answered by Penny Nom. 





Lines in the plane 
20011021 

From Greg:
*If the line with equation 3x4ky= 16 has yintercept 2, find k. *Write the equation of the line passing through (2,5) and perpendicular to the line passing through (2,4) and (6,1) Answered by Penny Nom. 





The shortest distance from a point to a line 
20010605 

From Kat: Find the shortest distance from the given line. Round to the nearest tenth. (2,1) and x+5y+20=0 Answered by Penny Nom. 





Pyramids 
20010418 

From Kelly: I'm in tenth grade and I know that there's some formula for finding out the slope of the side of a pyramid. I thought it could be the pythagorean therom, but I'm not sure if this works. Please send me the formula as soon as possible, I need it for a project. Answered by Penny Nom. 





Blood flow and age 
20010111 

From Gayle: I don't understand the second part of this problem Here is the first part that was correct. A 35yr old has 100% blood flow. A 65yr old has 64% blood flow. Find the rate of change per yr in the percent of blood flow. (This part is correct) m=(64100)/(3565)= 36/30= 1.2 per year of blood flow. Now, here is the second part I DON'T UNDERSTAND! .Let b represent the percent of blood flow and a represent a person's age. Write an equation that you could use to predict the percent of blood flow for a person of any age over 35. Answered by Penny Nom. 





A lampost and its shadow 
20001224 

From Laura: A lamppost line EC casts a shadow line AC. A 30 cm ruler line DB has been moved from A so that it's shadow falls just within the shadow of the lamppost.  Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?
 Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?
Answered by Penny Nom. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





Three points on a line 
20000825 

From Casey: I am trying to find the slope and yintercept of an equation. I have THREE x values and THREE y values. How do you do it? Help! Answered by Penny Nom. 





Slope 
20000819 

From John K. DePonte: My question is to why the variable "m" was chosen to represent the slope of a linear equation. I always told my class to think of "m" for "m"ountain slope. But what is the real reason for this? Answered by Penny Nom. 





Angle of Intersection of Two Lines 
20000302 

From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston. 





Two calculus problems 
19991201 

From O'Sullivan: Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help. I've set up a ratio and tried to find the constant but am stuck. Question #2 The figure shows a lamp located three units to the right of the yaxis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (5,0) is on the edge of the shadow, how far above the x axis is the lamp located? The picture shows an x and y axis with only the points 5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5. Answered by Harley Weston. 





Why is slope designated m? 
19990818 

From Peter Komlos: Why is the slope of a line is designated by the letter "m"? Answered by Penny Nom. 





A calculus problem 
19990722 

From Nicholas Lawton: The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the xaxis. the point (0,9) is on the curve. Find the values of p,q and r. Answered by Harley Weston. 





Slopes of curved lines 
19990609 

From Stephen Ehrler: When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Answered by Harley Weston. 





Parallel and perpendicular lines 
19990423 

From Crystal Pilling: My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x  5y= 16, (5,6) I have to find a line that is perpindicular to this line on a graph. HELP ME PLEASE!!!!! Answered by Penny Nom. 





y=mx+b 
19990415 

From Selena Royle: When solving a problem on slopes,and in the formula y=mx+b what do the M and B stand for? Why M and B? Answered by Penny Nom. 





0/11 
19990309 

From Jacob: What is the term applied to 0 divided by a number. In calculating slope problem my answer was 0 divided by 11. I don't know what to do with this answer or how to interpret it. Answered by Jack LeSage and Penny Nom. 





Equation of a line 
19970408 

From Susan Gregson: I am a secondary school teacher. My students and I would like to know why the letters m and b are traditionally used to stand for slope and Yintercept in the standard form of an equation. Was this an arbitrary choice? Who made it? Are the letters from Greek ot Latin words? Answered by Harley Weston. 

