Lines and the Coordinate Plane: Slope of a Line

Problem Solving Using Slope

 

As you saw at the beginning of the lesson, slope has many practical purposes.  Now you will have a chance to apply what you’ve learned in this section to problem solve. Slope is particularly useful for finding the average rate of change.

Example 1

In 1896, the winning time in the men’s Olympic 100 meter dash was 12 seconds.  In 1964, the winning time was 10 seconds.

What is the average rate of change, in seconds per year, between 1896 and 1964?

There are two points in the problem: (1896, 12) and (1964, 10).  Apply the slope formula.

m equals y 2 minus y 1 divided by x 2 minus x 1, m equals 10 minus 12 divided by 1964 minus 1896, m equals negative 2 divided by 68, m equals negative 1 divided by 34, which is approximately equals to -0.029

So, the average rate of change was -0.029 seconds per year.

Example 2

Bakery A sold 300 cupcakes in 12 days and sold 450 cupcakes in 18 days.
Bakery B sold 120 cupcakes in 5 days and sold 200 cupcakes in 8 days.

Which bakery had the greatest rate of increase (steepest slope)?

Bakery A Bakery B
m equals 450 minus 300 divided by 18 minus 12, m equals 150 divided by 6, m equals 25 m equals 200 minus 120 divided by 8 minus 5, m equals 80 divided by 3, m is approximately equal to 26.67


Bakery B had the greatest rate of increase, and would therefore have the steepest slope.