3-3 Rate of Change & Slope Objectives: 1. Use rate of change to solve problems 2. Find the slope of a line 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.

Daredevil Drop The Daredevil Drop at Wet’N Wild Emerald Pointe in Greensboro, North Carolina, is a thrilling ride that drops you 76 ft down a steep water chute. A rate of change of the ride may describe the distance a rider has fallen over a length of time. How can you write the rate of change? What might the ratio be for a ride with a rate of change of 2? Which has a steeper waterchute, a ride with a rate of change of 1 2 or a ride with a rate of change of 5 2 ?

Rate of Change A ratio that describes, on average, how much one quantity changes with respect to change in another quantity.

Example 1: Use the table to find the rate of Change Example 1: Use the table to find the rate of Change. Then explain its meaning.

Many real-world situations involve rates of change that are not constant

Example 2: Refer to the graph Example 2: Refer to the graph. Without calculating , find the 2-year period that has the least rate of change. Then calculate to verify your answer.

A rate of change is constant for a function when the rate of change is the same between any pair of points on the graph of the function. Linear functions have a constant rate of change.

Example 3: Determine whether each function is linear. Explain. a) b)

Slope The slope of a non-vertical line is the ratio of the change in the y-coordinates (RISE) to the change in the cx-coordinates (RUN) as you move from one point to another. Slope describes A rate of change How steep a line is The greater the absolute value of the slope – the steeper the line

Example 4: Find the slope of a line that passes through each pair of points

Example 4: Find the slope of a line that passes through each pair of points b) −4, −2 , (0, −2)

1. The first animated film to be nominated for an Oscar for best picture was Disney’s…? Beauty and the Beast Trivia… 2. What is the oldest major soft drink in America? Dr. Pepper in 1885 3. What is the most popular Jelly-belly flavor? Buttered Popcorn

Example 4: Find the slope of a line that passes through each pair of points

Example 4: Find the slope of a line that passes through each pair of points

Example 5: Find the value of 𝑟 so the line that passes through each pair of points has the given slope. a) 𝑟, −6 , 5, −8 ;𝑚=−8

Practice WS

Homework Pages 177 – 178: 14-19, 23, 24, 27-29, 35, 37, 39