Question

You arw keeping track of the amount you are charged for parking. On Monday, you are charged $47 after parking for six hours. On Tuesday, you park for three hours and are charged $32. If the amount charged for parking C is a linear relationship with the number of hours parked P, write an equation to model this situation.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given data values

STEP 2: Write the slope-intercept form for the equation of a line

`\begin{gathered} y=mx+b \\ where\text{ m is the slope and b is the y-intercept} \end{gathered}`

STEP 3: Find the slope m

`m=(y_2-y_1)/(x_2-x_1)=(47-32)/(6-3)=(15)/(3)=5`

STEP 4: Get the linear equation

`\begin{gathered} (y-y_1)=m(x-x_1) \\ Using\text{ point \lparen6,47\rparen} \\ By\text{ substitution,} \\ (y-47)=5(x-6) \\ y-47=5x-30 \\ y=5x-30+47 \\ y=5x+17 \end{gathered}`

where y is the amount charged for parking and x is the number of hours parked

Hence, the equation to model the situation is given as:

`C=5P+17`