Question

I need to know what the answer is and how to solve it

Answer 1

Since all information given about rental time is in hours and about rental cost is in dollars, so the unit for rental time is hours and for rental cost is dollars.

The cost for 2 hours is $20, so the given value 1 for rental time is 2 and for rental cost is 20.

The cost for 10 hours is $68, so the given value 2 for rental time is 10 and for rental cost is 68.

To calculate the slope m between two points (x1, y1) and (x2, y2) we can use the formula below:

`m=(y_2-y_1)/(x_2-x_1)`

So, using the points (2, 20) and (10, 68), we have:

`m=(68-20)/(10-2)=(48)/(8)=6`

Then, to calculate the y-intercept, let's use the point (2, 20) in the slope-intercept form of the equation:

`\begin{gathered} y=mx+b \\ 20=6\cdot2+b \\ 20=12+b \\ b=20-12=8 \end{gathered}`

So the expression to calculate the rental cost y after x hours is:

`y=6x+8`

For question 1, let's use x = 8 and calculate y:

`\begin{gathered} y=6\cdot8+8 \\ y=48+8 \\ y=56 \end{gathered}`

So the cost is $56.

For question 2, let's use y = 50 and calculate x:

`\begin{gathered} 50=6x+8 \\ 6x=50-8 \\ 6x=42 \\ x=7 \end{gathered}`

So we can rent for 7 hours.