8.5. Lesson 7- Compare Linear Functions

8.5. Lesson 7- Compare Linear Functions

Students compare the properties of two functions that are represented in different ways via tables, graphs, equations, or written descriptions.

​

​

Multiple Choice

BELL WORK:

Find the slope and y-intercept of this graph

• Slope: 1/2

  Y-Intercept: -2

• Slope: 2

  Y-Intercept: 2

• Slope: -2

  Y-Intercept: 4

• Slope: -1/2

  Y-Intercept: 0

It is very important for this lesson that you remember how to find the slope and the y intercept.

Let's Review

• functions are equations where any input value (often x) has only 1 output value (often y)

• You can represent a function as a graph, table or an equation

• If you have a graph you can use the vertical line test to check if it is a function

Comparing Constant Rate of Change

you can compare two linear functions by comparing their constant rate of change (their slope)

​

​

The other factor you can be asked to look at in the problems is the initial (beginning) value. Because the initial value is going to be where the input (x) is 0, it will be the y intercept on a graph or in an equation OR in a table.

​

Initial Value​

​

Multiple Choice

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which of the following is not a function?

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Select

Select all the linear functions. Think carefully.

• y=2x+7

• 3x+7y=10

• x=2

• $$3x^2+7y=2$$  

• $$3^3+7y=2x$$  

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Who is going at a faster rate and why?

• The tortoise because it got a head start

• The hare because its line is more steep

• They are going the same speed because the lines crossed

• I don't know

Multiple Choice

Which kitten grows fastest? What is it's rate of change?

• Kitten A with a rate of change of 3

• Kitten B with a rate of change of 4

• Kitten A with a rate of change of 4

• Kitten B with a rate of change of 3

Multiple Choice

Which tree was the tallest when it was first planted?

• Tree A
• Tree B
• Tree C

Multiple Choice

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for 8 movies in one month?

• Beth's service ($38 vs. $40) is cheaper
• Nate’s service ($42 vs. $44) is cheaper
• Nate’s service ($38 vs. $40) is cheaper
• Beth's service ($42 vs. $44) is cheaper

Multiple Choice

What is the initial value in this equation?
y=8x+6

• 8
• 6

Multiple Choice

Find the rate of change

• 3
• -3
• 20
• Not a constant slope/Non-Linear

Multiple Choice

Tim bought a new phone. He paid $125 on the day of purchase, then $50 per month until it was paid off. What is the initial value in this situation?

• 50

• 125

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Multiple Choice

What is a possible scenario for the given table?

• You have $8 and get $5 more each day!

• You have $16 and get $2 more each day!

• You have $2 and get $6 more each day!

• You have $6 and get $2 more each day!

Multiple Choice

Which function has the GREATEST initial value?

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts
• Ryan's Rafts

Multiple Choice

Which company should you use if you rent the raft for 9 hours?

• Water's Edge Rafts

• Ryan's Rafts

Multiple Choice

What has the GREATER rate of change.

• y = 7x + 10

• Someone who starts with $6 and gets $8 each day.

• y = 5x + 20

• Someone who starts with $8 and gets $6 each day.

Multiple Choice

Who is losing weight faster?

• Valerie

• Oscar

• Mrs. Conte

• They are losing the same amount of weight