Question

Ashley compares the fees charged by two babysitting agencies.The fees are shown below. Determine which function is described in the table below.Drag-and-drop either agency A or agency B into each box to correctly identify which function is described.​

Answer 1

Agency A: y = 12x

So Agency A pays a rate of $12 per hour

Agency B: y = 10x + 20

So Agency B pays an initial fee of $20 plus a rate of $10 per hour.

Explanation:

Agency A

To create a straight line equation for the data in table, use
`y = mx + b`, where m is the slope and b is the y-intercept.

To find the slope m, take 2 points from the table and use the slope formula.

Let
`(x_1,y_1)` = (3, 36)

Let
`(x_2,y_2)` = (5, 60)

Slope formula:
`m=(y_2-y_1)/(x_2-x_1)=(60-36)/(5-3)=12`

Now use the point-slope formula to create the final equation:

`y-y_1=m(x-x_1)`

`\implies y-36=12(x-3)`

`\implies y=12x`

Therefore, Agency A pays a rate of $12 per hour.

Agency B

From inspection, the function is a straight line.

Therefore we can use the straight line equation
`y = mx + b`,

where m is the slope and b is the y-intercept.

From inspection, we can see that the line crosses the y-axis at (0,20). Therefore, the y-intercept is 20.

`\implies y=mx+20`

Taking 2 points on the line and using the slope formula to find the slope m:

Let
`(x_1,y_1)` = (0, 20)

Let
`(x_2,y_2)` = (3, 50)

Slope formula:
`m=(y_2-y_1)/(x_2-x_1)=(50-20)/(3-0)=10`

Therefore, the final equation is:
`y=10x+20`

Therefore, Agency B pays an initial fee of $20 plus a rate of $10 per hour.