The cost of driving a car includes both fixed costs and mileage costs. Assume that it costs $163.40 per month for insurance and car payments and $0.23 per mile for gasoline, oil and routine maintenance.

(a) Find the values for m and b so that y=mx+b models the monthly cost of driving the car x miles.
(b) what does the value of b represent?

Question

The cost of driving a car includes both fixed costs and mileage costs. Assume that it costs $163.40 per month for insurance and car payments and $0.23 per mile for gasoline, oil and routine maintenance.

(a) Find the values for m and b so that y=mx+b models the monthly cost of driving the car x miles.
(b) what does the value of b represent?

anonymous · Answer

Recall that y=mx+b is the formula for a line. M is the slope of the line, and b is the y intercept (where the line crosses the y axis). You have a problem that gives 2 values; one is a fixed cost, and one is a variable cost. Think bout how they might best fit into the linear equation.

anonymous · Answer

Here is a hint: What is the cost of driving if you drive 0 miles?

anonymous · Answer

Okay so then m=0.23 and b=163.40

anonymous · Answer

Right!

anonymous · Answer

0.23

anonymous · Answer

0 miles means x=0. And if you carefully reread, there is a base cost before we add in additional cost per mile.

anonymous · Answer

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anonymous · Answer

Just owning the car will cost you a fixed ammount each month (b). Every additional mile costs 23 cents, so we add the variable cost to the fixed cost. As x increases, the cost goes up at a steady rate (.23 (our slope)) .

anonymous · Answer

oh ok i get it now thank you

anonymous · Answer

welcome!