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?