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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.

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SOLUTION

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

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

STEP 3: Find the slope m

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{47-32}{6-3}=\frac{15}{3}=5[/tex]

STEP 4: Get the linear equation

[tex]\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}[/tex]

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:

[tex]C=5P+17[/tex]

Ver imagen MireilleT600925

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