Proportional Relationships Answers

The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?

The table of values below represents a linear function and shows the amount of money in a tip jar at a dry cleaners since the dry cleaners opened for the day. How much was in the tip jar when the dry cleaners opened?Amount of Money in a Tip Jar at a Dry CleanersNumber of Hours Since Dry Cleaners Opened45678Amount of Money in Tip Jar ($)15.5018.2521.0023.7526.50

Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?Richard’s Distance Past the Start LineTime (minutes)510152025Distance (kilometers)2.83.44.04.65.2

Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B?

Corinne and Aretha are having a 26-mile race. Corinne gave Aretha a head start by letting her begin 3.5 miles in front of the start line. Their distances past the start line as the race has progressed can be represented by linear functions and are shown in the table and graph below. How many minutes after the start of the race will Corinne catch Aretha?Corinne’s Distance Past the Start LineTime (minutes)1020304050Distance (miles)1.252.53.755.06.25

The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?Amount in Juanita’s Savings AccountNumber of Months Working at Part-Time Job02468Amount in Savings Account (in dollars)$36$60$84$108$132

Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?Mary’s Cup-Filling ProgressTime (minutes)0.511.522.5Cups Remaining9981634527

The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer. What is the initial value?

The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, and why?x036912y37111519

Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice’s race?Antonio’s Distance Past the LandmarkTime (seconds)812162024Distance (meters)2941536577