Rate of Change A ratio (fraction) of the amount of change in the dependent variable (output) to the amount of change in the independent variable (input) Rate change in output (y) Of = change in input (x) Change

Example 1 page 77 Day 1 Day 2 Day 3 Day 4 1 3 6 8 15 45 90 120 Number of lawns 1 3 6 8 Amount earned 15 45 90 120 Independent variable (x) → number of lawns Dependent variable (y) → amount earned Change in $ 45 – 15 = 30 90 – 45 = 45 120 – 90 = 30 all equal to Change in lawns 3 – 1 = 2 6 – 3 = 3 8 – 6 = 2 $15 per lawn These Rates of Change are constant since they are all the same. If Rates of Change are not the same, they are said to be variable

Your Turn page 77 Answer the “Your Turn” question with a partner

Using graphs to find Rate of Change Explore activity page 78 Do steps A thru D and answer Reflect questions 2 & 3

Calculating Slope (m) page 79 When the rate of change of a relationship is constant, any segment of its graph has the same steepness. This constant rate of change is called the slope of the line The slope of a line is the ratio (fraction) of the change in y-values over the change in x-values slope (m) = y2 – y1 x2 – x1 you can also find slope by using two points on a graph and finding the rise over the run between the two points slope (m) = vertical change (rise) horizontal change (run)

Your Turn page 79 Do “Your Turn” on page 79 with a partner

Assignment #1 – 8 page 80 #10 – 18 evens pages 81 & 82