Question

Angel rented a car and drove 300 miles and was charged $120. On another week, she drove 560 miles and was charged $133. Using miles on the horizontal axis and cost on the vertical axis (miles, cost), which of the following choices is the correct linear equation?

A) (y = 0.25x + 90)
B) (y = 0.2x + 100)
C) (y = 0.15x + 105)
D) (y = 0.2x + 90)

Answer 1

The correct linear equation for the car rental charges based on the given data (300, $120) and (560, $133) is y = 0.05x + 105. This indicates a charge of $0.05 per additional mile driven, with a base charge of $105. However, none of the options (A, B, C, D) provided match these calculations.

Step-by-step explanation:

To determine the correct linear equation for Angel's car rental charges, we need to use the given data points to find the slope (rate per mile) and the y-intercept (base charge). We have two data points: (300, $120) and (560, $133). To calculate the slope (m), we use the formula:

m = (y2 - y1) / (x2 - x1)

m = (133 - 120) / (560 - 300) = 13 / 260 = 0.05

This means Angel is charged an additional $0.05 per mile driven. We can then use one of the points to find the y-intercept (b) for the equation y = mx + b.

120 = 0.05(300) + b

120 = 15 + b

b = 120 - 15

b = 105

So the correct equation, with the base charge as the y-intercept and the rate per mile as the slope, is:

y = 0.05x + 105

This equation does not match any of the provided options A to D. It appears that there may be a typo in the options given, as none of them reflect the correct calculations based on the data provided.