Question

Carolina is mowing lawns for a summer job. For every lawn mowed, she charges a fixed amount plus $\$6$ for each hour of work. Her total fee for a $4-$hour job is $\$32$. Which of the following is the correct slope-intercept equation for the given situation?

• A. $6y=4x+32$
• B. $y=6x+8$
• C. $y=4x+6$
• D. $32y=6x+4$

Answer 1

The correct option is B $y=6x+8$

Detailed step-by-step solution:

Carolina is mowing lawns for which
she charges an initial fee which is a fixed amount for the entire duration of work. This amount is not directly given.
she charges $\$6$ for every hour she works. This is an amount which will decide how the total amount increases as she works for multiple hours.

Now, we want to express this in slope-intercept form which would be of the form
$y=mx+b.$ Here, $y$ will represent the total cost and $x$ will represent the number of hours Carolina mows the lawn.

Since $\$6$ is the amount charged for every additional hour, the slope $m$ is $6$. The slope-intercept form of the equation can be written as
$y=mx+b$
$\Rightarrow y=6x+b$ (the slope being $6$)

We also know that the total cost for $4$ hours is $\$32.$ We can use this in the equation to find the value of b which represents the fixed amount Carolina charges.
$y=6x+b$
$\Rightarrow 32=6\times 4+b$ (substituting for $x$ and $y$ to find $b$)
$\Rightarrow 32=24+b$
$\Rightarrow 32-24=b$
$\Rightarrow b=8$ (switching sides. We now also replace the value of $b$ in the equation)
$\Rightarrow y=6x+8$

Therefore, the slope intercept for the given equation is $y=6x+8,$ which is option A.

$\Rightarrow$ Option A is correct.