5.3 Rate of Change and Slope 5.4 The Slope Formula Algebra 5.3 5.3 Rate of Change and Slope 5.4 The Slope Formula

5.3 Learning Targets Language Goal Students will be able to verbally relate a constant rate of change to the slope of a line Math Goal Students will be able to find rates of change and slopes. Essential Questions Why are graphs a valuable source of information?

5.3 Warm-up

5.2 Homework Check

5.2 Homework Check

5.2 Homework Check

5.3 Vocabulary Rate of Change: Rise: Run: Slope: A ratio that compares the amount of change in a dependent variable to the amount of change in a independent variable The difference in the x-values of two points on a line. The difference in the y-values of two points on a line. The ratio of rise to run for any two points on a line.

Rate of Change and Slope

Rate of Change Practice The table shows the temperatures (in °F) at one location at different times. 1. Which is the dependent variable? 2. Which is the independent variable? 3. Calculate the rate of change for each time interval. 8 am to 11 am: ______ 11 am to 1 am: ______ 1 pm to 5 pm: _______

Hint!! The independent variable is usually a form of time!!!

Example 1: Word Problem The table shows a truck driver’s distance from home during one day’s deliveries. Find the rate of change for each interval. Hour 0 to Hour 1: ____ Hour 1 to Hour 4: ____ Hour 4 to Hour 5: ____ Hour 5 to Hour 8: ____ Hour 8 to Hour 10: ____ The rate of change represents the average speed. During which time interval was the driver’s average speed the least?

Example 2: Finding Rates of Change from a Graph The table shows the amount of water in a pitcher at different times. Graph the data and show the rates of change. Between which two hours is the rate of change the greatest?

Example 3 and 4: Finding Slope From a Graph 𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

Example 3 and 4: Finding Slope From a Graph 𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

Example 3 and 4: Finding Slope From a Graph 𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

Classifying Slopes

Example 5: Describing Slope As the absolute value of the slope increases, the lines becomes steeper. A. m = 0 B. m = 1 50 C. m = -10 D. m = 2 0

Extra Practice Finding Slope WS Work with a partner or individually. We will discuss as a class. Make sure that you find a point that lies on an intersection between an x and y integer.

Calculate Slope Given Graph

Calculate Slope Given Graph

Calculate Slope Given Graph

Calculate Slope Given Graph

Calculate Slope Given Graph

Calculate Slope Given Graph

5.3 Lesson Quiz