Graphing lines can
be accomplished by any of the following methods:
create a table of values by choosing values for
x and working out the values for y. Plot the resulting
points and join them with a straight line.
Ex. y = 2x - 1
x: -2, -1, 0, 1, 2
y: -5, -3, -1, 1, 3
plot (-2, -5), (-1, -3), (0, -1), (1, 1), and (2, 3) and join them
with a straight line.
find the x-intercept and y-intercept and join them
with a straight line
Ex. 3x + 4y = 12
x-int: 3x = 12 y-int: 4y
x = 4 y
Plot (4, 0) Plot
Now join these 2 points to get the line.
determine the slope and y-intercept of the line,
plot the y-intercept and find a second point on the line by moving
vertically and horizontally according to the rise/run of the slope.
Ex. y = 3x + 5 slope = 3
(or 3/1 in "rise over run" form), y-intercept = 5
the point (0, 5).
up 3 units and to the right 1 unit from the y-intercept. Plot a second point
join these two points to get the line.
To graph a linear inequality, follow the following steps:
Replace the inequality sign with an equal sign and
graph the resulting line.
- If the inequality is a greater than (>) or
a less than (<) you will graph the line as a dotted line.
- If the inequality includes "or equal to" as
in "greater than or equal to", you graph the line as
a solid line.
Choose a point on one side of the line (not on the
line!) and substitute the coordinates into the inequality
you started with.
- If you get a true mathematical statement
(like 4<9), then you want to shade the side of the line that
contains the point you used to do the test.
- If you get a false mathematical statement (like
0>3), then you want to shade the side of the line that does
not contain the point you used to do the test.
Hope this helps,