The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her $\$ 200$ to drive 300 mi and in July it cost her $\$ 350$ to drive 600 mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.
A) $C=-50 d+0.5$
B) $C=-50 d-0.5$
C) $C=0.5 d+50$
D) $C=2 d+50$
E) $C=0.5 d-50$

Question

Quizplus · Accepted Answer

The cost function is linear, and we can find the slope (m) using the formula $m = \frac{\Delta C}{\Delta d} = \frac{350 - 200}{600 - 300} = \frac{150}{300} = 0.5$. The y-intercept (b) can be found using one of the points, e.g., $200 = 0.5(300) + b$, which gives $b = 50$. Thus, the function is $C = 0.5d + 50$.

The Monthly Cost of Driving a Car Depends on the Number