Finding Rate of Change (With the Graph) King/Halling Algebra 2011-2012

AIM What is the rate of change and how do we use it? How does a graph tell us about the relationship between the variables graphed? TOPIC: Rates of Change (Graphically)

DO NOW # of Absences Average Grade 90 2 85 4 80 6 75 90 2 85 4 80 6 75 Generate a function rule for the given table Explain what the rate of change of the function means. Is the rate of change positive or negative? Why?

What Does It Mean? Positive Rate of Change Negative Rate of Change When is the rate of change positive? What does a positive rate of change mean? Brainstorm a scenario that would generate a positive rate of change. Negative Rate of Change When is the rate of change negative? What does a negative rate of change mean? Brainstorm a scenario that would generate a negative rate of change.

Calculating Slope The rate of change is also known as the slope We use the term slope when graphing lines Slope: The ratio of the vertical change to the horizontal change slope = change in y = vertical change _ = Rise_ change in x horizontal change Run

Find the Slope Remember: Pick any two points and count boxes!! slope = vertical change horizontal change Rise__ Run Pick any two points and count boxes!!

Try These! Find the Slope

More Practice

Pick useful points! (Use whole numbers) Slopes as Fractions Pick useful points! (Use whole numbers)

Exit Ticket - 5 Pts When is the slope of a line negative? - 1 When is the slope of a line positive? - 1 When is the slope of a line zero? - 1 What is the slope of the line graphed at the right? - 2

Homework Homework #12: Pg. 312 #3-9