Question

Trisha is throwing a pool party to kick off the summer. Her pool is empty, so she starts filling it with water from a garden hose. This table shows the relationship between the time Trisha has been filling up the pool (in minutes), x, and the volume of water in the pool (in gallons), y. x (minutes) y (gallons) 2 34 3 51 4 68 5 85 According to the values in the table, do x and y have a proportional relationship? yes no

Answer 1

Answer: Yes

Step-by-step explanation

I'll assume the table looks like this

`\begin{array}c \cline{1-2}\text{x} & \text{y}\\\cline{1-2}2 & 34\\\cline{1-2}3 & 51\\\cline{1-2}4 & 68\\\cline{1-2}5 & 85\\\cline{1-2}\end{array}`

If so then we divide each y value over its paired x value.

• y/x = 34/2 = 17
• y/x = 51/3 = 17
• y/x = 68/4 = 17
• y/x = 85/5 = 17

We get the same result (17) each time, which confirms x and y have a proportional relationship

The constant of proportionality is k = y/x = 17. That rearranges to the equation y = 17x. This equation is of the form y = kx.

For example, if x = 2 minutes go by then the pool will have y = 17x = 17*2 = 34 gallons of water. I'll let you try out the other x values.