4.06 Identifying proportional relationships

For each of the following table of values:

Consider the points plotted on the coordinate plane:

Consider the points plotted on the coordinate plane:

A physiotherapist charges \$55 per patient she treats. The following table shows her weekly income:

While filling a pool 72 \text{ cm} deep, Victoria notices it has taken 3 hours to fill it up to a depth of 36 \text{ cm}.

The volume V of a rectangular prism can be calculated by the formula V = l w h, where l is the length, w is the width and h is the height of the prism.

If the length, width and height of the prism are doubled, how is the volume affected? Explain your answer.

Homer is making cups of fruit smoothie. The amount of bananas and strawberries he uses is shown in the table:

Consider the following table where y represents the total rent paid on a house that has been rented for x weeks:

For every 6 minutes that Emma runs, she covers 850 \text{ yd}. Let y represent the distance Emma runs in x minutes. Write an equation relating x and y.

Frank serves 8 cups of coffee every 9 minutes. Using y for the number of cups of coffee and x for the amount of minutes that have passed, write an equation relating x and y.

A courier’s delivery charges are outlined in the following table:

The admission prices to an amusement park are set out in the following table:

During a gym session, participants can either do full push-ups (on toes) or half push-ups (on knees). However since half push-ups are easier, those who choose this option will need to do more of them. The table shows how many full and half push-ups participants had to do:

The coordinate plane shows the parking fee for various numbers of hours parked:

At a ski resort, you can purchase lift passes according to the number of days you wish to ski. For example, if you want to ski for 3 days you could purchase a 3-day lift pass, or a 2-day lift pass and then a 1-day lift pass. The lift pass prices are shown on the following graph:

In developing countries, one important goal is to improve access to education. A new initiative is aimed at building new schools over a period of time. The table shows the number of new schools, y, built x months after starting the initiative:

Consider the two following investment methods:

• Method A: Deposit \$4000 into an account immediately and add \$40 at the end of each month thereafter.

• Method B: Deposit \$80 at the end of each month.

Amy and Vanessa have used two different investment strategies to enhance their savings. The amount of interest each has earned after t years is presented in the table and graph: