Lesson 3: 3-3 Rate of Change and Slope
Duration of Days: 5
Lesson Objective
Use rate of change to solve problems.
Find the slope of a line.
What do we need to know in order to determine if the function is linear?
What is the ratio to find rate of change?
What can a linear graph tell you about the relationship that it represents?
rate of change
slope
F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
F.LE.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25
Rate of change is a ratio that describes, on average, how one quantity changes with respect to a change in another quantity. Slope can be used to describe rate of change. The slope of a line is the ratio of the vertical change to the horizontal change. The slope formula allows you to find the slope of a line without graphing.
The Daredevil Drop at Wet 'n Wild Emerald Pointe in Greensboro, North Carolina, is a water slide that drops riders 76 feet. A rate of change of the ride might describe the distance a rider has fallen over a length of time.
As students work through Example 6, watch for those who try to find the cross product mentally and forget to multiply both r and -4 by 3.
If students automatically assume that the left-most point has to be (x1, y1) and the point farther right is (x2, y2), then explain that the designation of (x1, y1) and (x2, y2) is arbitrary. Write pairs of points on index cards. Give one card to each student. Have them find the slope both ways. Then ask which way made the subtraction easier.
Extension: The road sign on a hill says 5% grade. The elevation of the road at that point is 1200 feet. Make a drawing of this situation. What would be the elevation of the road at an additional 2000 horizontal feet from the road sign?
Practice: Exercises 1 - 13
Exercises 53 -58
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