Math CentralQuandaries & Queries


Question from mitchell, a student:

Graph each equation.

y = 2x + 4

We have two solutions for you.

Hi Mitchell,

We can graph this equation using a few different methods, but we'll do the easiest one here.

Let's say I have an equation y = 5x - 11.  This equation is in Slope-Intercept Form (y = mx + b), which means that we know 2 special things that will help up to graph it.  Now, we know that the Slope of this equation is m, so it must be 5.  We know that b is the y-intercept (which is a point that is on the y-axis).  So b is -11.

Since -11 is our y-intercept we can plot that point on our graph (0,-11) and from there we use our slope to find other points...what do I mean?

Well, slope is = to rise/run.  So if our slope is 5, then I have a rise of 5 and a run of 1.  Now if we rise up 5 from (0,-11) and over 1, we will have a new point and with two points we can graph our line.

Hope that helps you,



Hi mitchell,

I'll give you another way to think about the graph. The graph of your equation y = 5x - 11 is the set of all pairs (x, y) in the coordinate plane that 'fit' the equation. (By 'fit' I mean that the x and y values when plugged into the equation make it true).

Given one of the coordinates of the ordered pair (x,y) on the graph, you can find the value of the other because the two are related by the equation y = 5x -11 . (We can plug the value we know into the equation, and then solve for the one we don't know. )

So, we can find some points on the graph if we choose some values for x, and then use the equation to find the values of the corresponding y coordinates.

An equation of the form you have given ( y = mx + b ) is always a straight line [WHY? You can think about this.] To draw a line, all we need is two points on the line. So, to graph your equation, find two points on the line, and then draw the line connecting them.


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