We want to complete the following given definition.

$\underline{?}$ is the change in $y$ divided by the change in $x .$

Let's plot two example points in the coordinate plane and then connect them with a line.

If we want to determine the steepness of the line, we should examine how the $y -$ and $x -$ values change as we move along the line. Let's consider the change in $x -$ values first. Recall that the change in $x -$ values is called the $run .$ The run tells us about the horizontal distance between the points.

Next, the change in the $y -$ values is called the $rise .$ The rise describes the vertical distance between the points.

Now, the steepness of the line or segment is the ratio of rise and run. The steepness is also called the slope.

Slope = \frac{Rise}{Run}

In other words, we can say that the slope is the change in

y -

values divided by the change in

x -

values. For our example line, the run is

4

units and the rise is

2

units, so the slope is

\frac{2}{4},

or

0.5 .

Finally, we are ready to complete our definition.

$\underline{Slope}$ is the change in $y$ divided by the change in $x .$

Exercise