Expert: Josh - 1/17/2008

Question
a line who's change in y is 500 when x sub 1 =8 and x sub 2 = 17

Answer
Hi Adam

I believe the vertical and horizontal axes are labeled x_2 and x_1. Why don't we call them y and x instead.

The slope-intercept form looks something like this: y = mx + b, where m represents the gradient (also called slope, or rise over run, change in y divided by change in x); b is the point where the line crosses the vertical y-axis.

Given a coordinate (say, xo=8 and yo=17), we can write the equation as (y-yo)=m(x-xo). We can write this as (y-17)=500(x-8). To see why this works, observe that the expression is true if we substitute x=8 and y=17 for the x and y variables. We obviously get zero on the left hand side, and also the right hand side of the equation.

Now, it's a matter of rearranging the equation (y-17)=500(x-8) into the slope-intercept form.

Multiplying out the right hand side, we get
y-17=500x-4000. Adding 17 to both sides, we get y=500x-3983. The numbers are very unusual, as a change in y with respect to x of the magnitude of 500 is quite fast. The line is almost vertical.

I hope this answers your question.