The Slope of a Line

Look at the line below:

One property of a line is its "steepness." In algebra, steepness is defined by SLOPE.
 
By definition, slope = change in y/change in x. The change in y and the change in x are shown in the graph below.

Change in y = change in y coordinates = (-1-2) = -3
 
Change in x = change in x coordinates = (3-(-4)) = 7
 
So the slope of the line = -3/7

The slope of the line connecting the points (a,-1) and (-2,-2) is 1/7. What is a?

First, write out the equation for slope:

slope = change in y/change in x

Next, find the changes in y and x:

Change in y: -2-(-1) = -2+1 = -1
Change in x: -2-a  

Use these values in the equation for slope:

slope = -1/(-2-a) = 1/7

Solve for a:

-7 = -2 - a
a = 5