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

Answer:

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.

Step-by-step 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: $m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{60-36}{5-3}=12$

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: $m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-20}{3-0}=10$

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

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