Applications of Rates and Proportional

Reasoning: Rate of Change

Today you will learn to:• Calculate the rate of change from a graph

•Calculate the slope of a line

M7.A.2.2.1

Warm-up Problem: Unit Warm-up Problem: Unit Rates (Review)Rates (Review)Four friends took a road trip to visit the Smithsonian in Washington D.C. They drove 520 miles in 5 hours. What was their average speed, in miles per hour?

After their visit, they stopped at a sidewalk vender and bought 8 hotdogs for $4.00. What was the price per hot dog?

Rate of ChangeThe rate of change is the speed at

which a variable changes over a specific period of time. Graphically, the rate of change is represented by m, or the unit rate. To calculate the rate of change from a graph, determine how the change in y-values relates to the change in x-values.

In the graph to the left, Ally graphed her allowance over six weeks. Based on her graph, you can see that her allowance is $10 per week.

Slope of a LineWe sometimes refer to the rate of change

as the SLOPE of a line. Essentially, it the is the unit rate (m), or y ÷ x. To determine the slope of a line, and, therefore, the rate of change, check out the following videos (2) from the Khan Academy. It is important to note that the rate of change does NOT have to be proportional, and can be negative.

•Graphical Slope of a Line•Slope of a Line

Example: Rate of ChangeThe science club is inflating a model of a

hot air balloon, as shown in the graph below. At what rate is the diameter increasing?