8.4. Lesson 22- Revisiting Constant Rate

8.4. Lesson 22- CONSTANT RATE

Student Outcomes

- know that any constant rate problem can be described by a linear equation in two variables where the slope of the graph is the constant rate.

- compare two different proportional relationships represented by graphs, equations, and tables to determine which has a greater rate of change. 

Fill in the Blank

Lets review previous learning: Write the equation for this line.

Multiple Choice

Write the equation for this line.

• y=5/2x+11

• y=5/2x-11

• y=-5/2x+11

• y=2/5-11

Multiple Select

Erika set her stopwatch to zero and switched it on at the beginning of her walk. She walks at a constant speed of 3 miles per hour. Work in pairs to express this situation as an equation, a table of values, and a graph.

Check off each thing you have done ONLY when you completed ALL THREE on your paper.

• write an equation

• create a table of values

• sketch a graph

Use the table of values or the equation to create a line with the solutions

Multiple Select

What is the meaning of the 3 in the equation 𝑦 = 3x. Select all that apply

• slope

• rate

• rate of change

• constant

Fill in the Blank

A faucet leaks at a constant rate of 7 gallons per hour. Suppose 𝑦 gallons leak in 𝑥 hours from 6:00 a.m. Express the situation as a linear equation in two variables

Since we know that the faucet leaks at a constant rate, then we can write the linear equation in two variables as 𝑦/x = 7, which can then be transformed to y=7x

Again, take note of the fact that the number that represents slope in the equation is the same as the constant rate of water leaking. 

Open Ended

How can we determine the rate at which this faucet leaks?

Fill in the Blank

Using what you know about slope and constant rate, determine the rate the faucet leaks. M=___

Multiple Choice

Which faucet had the worst leak?

• the 1st because the rate of change the water leaked is more. 7 is a greater rate of change than 6.5

• the 1st because it leaks faster.

• the 2nd because it leaks faster

• the 2nd because it has a greater rate of change

Multiple Choice

The graph represents the rate at which Kristina can paint. Her sister Tracee paints at an average rate of 45 square feet in 12 minutes. Assuming Tracee paints at a constant rate, determine which sister paints faster. Choose the BEST answer.

• Tracee because she paints at a faster rate

• Kristina because her rate is 4 compared to Tracee's rate of 3.75.

• Kristina because she paints at a faster rate.

• Tracee because her rate of change is 45 which is greater than 4

Multiple Choice

Train A is represented by the graph.

Train B travels at a constant rate. The train travels at a rate of 95 miles every one and a half hours.

Which train travels faster and why.

• Train A because is has a greater rate

• Train A because it has a greater rate 60 is greater than 47

• Train B because it has a greater rate. 95 is greater than 3

• Train B because it has a greater rate. 63 1/3 is greater than 60

Multiple Choice

Company B offers a solar panel that produces energy at an average rate of 325 watts in 2.6 hours. Assuming solar panels produce energy at a constant rate, determine the equation that can be used to represent Company B.

• y=2.6x+325

• y=0.008x

• y=120x

• y=125x

Exercises (10 minutes) Students work in pairs or small groups to complete Exercises 1–5

Discuss exercise 5.

Open Ended

Explain your general strategy for comparing proportional relationships.

CLOSING : Can we, Do we now know??

• - know that any constant rate problem can be described by a linear equation in two variables where the slope of the graph is the constant rate.

  
  

• - compare two different proportional relationships represented by graphs, equations, and tables to determine which has a greater rate of change. 

Multiple Choice

Practice for Exit Ticket

Which choice best describes the difference between the rates at which the girls did jumping jacks?

• Melissa did 6 more jumping jacks per minute than Alicia.

• Alicia did 6 more jumping jacks per minute than Melissa.

• Melissa did 5 more jumping jacks per minute than Alicia.

• Alicia did 5 more jumping jacks per minute than Melissa.