5.3 RATE OF CHANGE AND SLOPE 5.4 THE SLOPE FORMULA Algebra 5.3.

5 .3 RATE OF CHANGE AND SLOPE5.4 THE SLOPE FORMULA

Algebra 5.3

5.3 Learning Targets

Language GoalStudents will be able to verbally relate a

constant rate of change to the slope of a lineMath GoalStudents will be able to find rates of change

and slopes.Essential QuestionsWhy 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=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

=h𝐶 𝑎𝑛𝑔𝑒𝑖𝑛 𝑦h𝐶 𝑎𝑛𝑔𝑒 𝑖𝑛𝑥

Example 3 and 4: Finding Slope From a Graph

𝑆𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

=h𝐶 𝑎𝑛𝑔𝑒𝑖𝑛 𝑦h𝐶 𝑎𝑛𝑔𝑒 𝑖𝑛𝑥

Example 3 and 4: Finding Slope From a Graph

𝑆𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

=h𝐶 𝑎𝑛𝑔𝑒𝑖𝑛 𝑦h𝐶 𝑎𝑛𝑔𝑒 𝑖𝑛𝑥

Classifying Slopes

Example 5: Describing Slope

As the absolute value of the slope increases, the lines becomes steeper.

A. m = 0 B. m =

C. m = -10 D. m =

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