Question

Harold and Harry both rented cars from Hurry Up Motors. Harold rented his car for 6 days andwas charged $194. Harry rented his car for 3 days and was charged $122. Choose theequation that represents y, the rental cost, in terms of x, the days of the rental.

Answer 1

Step 1:

Write the coordinates in terms of cost and number of days.

( cost , days )

Step 2

( 3 , 122 ) and ( 6, 194)

Step 3:

Find the slope

`\begin{gathered} \text{Slope m = }(y_2-y_1)/(x_2-x_1) \\ x_1\text{ = 3} \\ y_1\text{ = 122} \\ x_2\text{ = 6} \\ y_2\text{ = 194} \\ m\text{ = }\frac{194\text{ - 122}}{6\text{ - 3}} \\ m\text{ = }(72)/(3) \\ m\text{ = 24} \end{gathered}`

Step 4

Find the equation using the slope m and point 1

`\begin{gathered} m\text{ = }(y-y_1)/(x-x_1) \\ 24\text{ = }\frac{y\text{ - 122}}{x\text{ - 3}} \\ \text{y - 122 = 24(x - 3)} \\ \text{y - 122 = 24x - 72} \\ y\text{ = 24x - 72 + 122} \\ y\text{ = 24x + 50} \end{gathered}`

Final answer

The equation is y = 24x + 50