1. 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

2. Warm-up Problem: Unit 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?

3. Rate of Change The 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.

4. Slope of a Line We 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

5. Example: Rate of Change The science club is inflating a model of a hot air balloon, as shown in the graph below. At what rate is the diameter increasing?