Algebra 2 Name: ______

Linear Models Rayside

1.  A student is trying to figure out the relationship between the amount of studying he does and his score on a math test. Below is a chart that displays how many hours he studied for a test and the score that he got on that test.

Hours Studied / Score on Test
0 / 62
.5 / 70
1 / 78
2 / 94

Is there a linear relationship between the number of hour studied and his score on the test?

Write a linear model that explains the relationship between number of hours studied and score on the test (basically, use the data to write the equation of the line).

If the student needs to score a 100 on the next test in order to get a B+ for the year, how many hours should he study?

If the student only has 45 minutes to study for his next test, what grade should he expect on the test?

Explain what the slope of the line means in the context of the problem.

2.  Below is data taken from a person’s car. It displays the number of gallons of gas that have been used and the number of miles that the car can still travel on that tank of gas.

Gallons of gas used / Miles you can still travel
0 / 450
2 / 350
3 / 300
5 / 200

Is the relationship between the number of gallons of gas used and the miles that the car can still travel linear?

Write a linear model that explains the relationship between the number of gallons of gas used and the number of miles that you can still travel.

If a person has used 7.5 gallons of gas, how many miles can he still travel in the car?

If a person can travel for 125 more miles, how much gas have they used?

How much gas does this tank hold?

What does the slope of the line mean in the context of this problem?

3.  A company that manufactures bikes compiles the following data relating the number of bikes that it produces and the cost to produce those bikes.

Number of Bikes Produced / Cost to Produce
8 / 10,000
9 / 10,600
11 / 11,800
12 / 12,400

Write a linear model that explains the relationship between the number of bikes that are produced and the cost to produce those bikes.

What is the y-intercept of this linear model and what does it mean in the context of this problem?

How much will it cost the company to produce 24 bikes?

How much does it cost the company to produce each additional bike?

If the company can spend $35,000 this month making bikes, how many bikes can they produce?

4.  As a car ages, it’s value decreases. This is called depreciation. Below is a chart that shows the depreciation for a Honda CRV.

Age of the car (in years) / Value of the car
1 / 15,000
5 / 11,000
7 / 9,000
8 / 8,000

Is there a linear relationship between the age of the car and its value?

Write a linear model that explains the relationship between the age of the car and its value.

What does the slope of the line mean in the context of this problem?

What is the y-intercept and what does it mean in the context of the problem?

When the car is 6 years old, what will it’s value be?

You want to trade in your car that is 4 years old and the dealer offers to give you $11,700 for it. Are you getting a fair value for your car?