Question

Macy babysits the children in her neighborhood. For each family, she charges a flat fee plus a per hour charge as described by the data in the table.Which equation represents the total amount Macy charges for each family where x represents the number of hours she babysits? A. y = 4x + 71 B. y = 9x + 7 C. y = 4x + 36 D. y = 13x + 117

Answer 1

B. y=9x+

Explanation:

To deermine tehe equation, pick two pairs of points from the table.

• The points are (8, 79) and (12, 115)

Substitute these points into the lope-ointercept form of the equation of a line.

`y=mx+b`

At (8,79): x=8 and y=79

`79=8m+b`

At (12, 115): x=12 and y=115

`115=12m+b`

Solve the two equations siultaneously fror m and b.

`\begin{gathered} 79=8m+b \\ 115=12m+b \\ Subtract \\ -36=-4m \\ \implies m=(-36)/(-4)=9 \end{gathered}`

Next, substitute m=9 into the first equation to solve for b:

`\begin{gathered} 79=8m+b \\ 79=8(9)+b \\ b=79-72 \\ b=7 \end{gathered}`

Substitute m=9 and b=7 into the slope-intercept form:

`y=9x+7`

The equation that represents the total amount Macy charges for each family where x represents the number of hours she babysits is:

`y=9x+7`

Option B is correct.