In this investigation, you will be solving and interpreting several rate problems. Be sure to show your calculations.

Problem #1:

Look at the following graph of Carl’s travel time and distance:

What is Carl’s constant rate of speed (in miles per hour)? _____

How many miles will Carl have traveled after 2 hours?

Problem #2:

Look at the following equation:

–4x + y = 10

What is the slope of this line? _

What is the value of y when x = 3? _

Problem #3:

What is the rate (in dollars per ticket)?

How much money will the theater earn if it sells 150 tickets? __

Problem #4:

Karen is trying to choose a cell phone plan. Company J charges a subscription fee of $30 per month plus $1 per hour of use. Company K charges no monthly fee, but charges $2 for every hour of use.

Karen made the following graph to compare the prices of the two plans:

The lines for Company J and Company K cross at a point. The coordinate (30, 60) is the point at which Company J and Company K cost the same.

What does the point (30, 60) mean? (Hint: What is being graphed on the x-axis? What is being graphed on the y-axis?)

If Karen uses her cell phone for less than 30 hours a month, which company should Karen choose? Why?

If Karen uses her cell phone for more than 30 hours a month, which company should Karen choose? Why?

What does the point (30, 60) mean? (Hint: What is being graphed on the x-axis? What is being graphed on the y-axis?) (30,60) is equal to x=30 and y=60.

If Karen uses her cell phone for less than 30 hours a month, which company should Karen choose? Why?

I think that Karen should use Company K because if she uses Company J, there would already be an extra fee of $30 from the monthly payment. Instead, Company K doesn’t have the monthly payment plan, but the hourly price is two times pricier but cheaper. To make it simple, let’s say Karen use her phone for about 25 hours for the whole month.

Company J: $30 + $25(1) = $55

Company K: 25(2) = $50