Question

The cost for a mechanic increases linearly as the number of hours needed to fix a car increases. A mechanic worked 5 hours and charged $375. The same mechanic worked 12 hours and charged $795.

Write an equation that describes the relationship.

a) C = 75h + 150
b) C = 90h + 225
c) C = 75h + 375
d) C = 45h + 225

Answer 1

The correct linear relationship equation based on the information provided is C = 60h + 75. This equation is not listed among the options given in the student's question; hence none of the options (a, b, c, d) are correct.

Step-by-step explanation:

The relationship between the hours worked by the mechanic and the cost charged can be determined using a linear equation. Based on the information provided, we are given two points: (5, $375) and (12, $795). We can calculate the slope, which is the rate per hour, using the formula slope (m) = (y2 - y1) / (x2 - x1). That gives us (795 - 375) / (12 - 5) = 420 / 7 = 60. This indicates that the mechanic charges $60 per hour. Next, we can use the point-slope form to find the y-intercept (b) by substituting the slope and one of the points into the equation y = mx + b. Using the point (5, $375), we get $375 = 60(5) + b, which simplifies to $375 = $300 + b. Subtracting $300 from both sides yields $75 for b. The linear equation representing the relationship of cost to hours is C = 60h + 75.

Thus, none of the options provided in the student's question correctly reflects this relationship. If we were to substitute the given options into our scenario, each would yield different rates and y-intercepts than those that we have calculated.