Answer
a) $C=\frac{1}{4}x+260$
b) $\$635$
c) See image for graph. The slope represents the cost to drive each mile.
d) The C-intercept ($\$260$) represents the cost to have the car even without driving.
e) A linear function is suitable because a car's average gas mileage and cost to operate is generally consistent.
Work Step by Step
a) We have two points: $(480, 380)$ and $(800, 460)$. Find the slope.
$m=\frac{C_2-C_1}{d_2-d_1}=\frac{800-480}{460-380}=\frac{1}{4}$
Now use point-slope form and solve for $C$.
$C-380=\frac{1}{4}(d-480)$
$C=\frac{1}{4}d+260$
b) Plug $1500$ into $d$
$C=\frac{1}{4}(1500)+260=\$635$
c) Graph the equation found in part (a). The slope represents the rate of change of a function, which in this case is how much the cost changes per mile.
d) C-intercept is 260. The y-intercept represents the y-value when x=0, which in this case is the cost when no miles are driven.
e) A linear function is suitable because a car's average gas mileage and cost to operate is generally consistent.
