finding the value for y=mx+b

Question

The cost of driving a car included both fixed costs and mileage costs.  Assume that it costs 174.20 per month for car insurance and car payments and .29 per mile for gas, oil and repairs.

a) find the values for m and b so that y=mx+b models the monthly cost of driving the car with x miles

b) what does the value of b represent

Answer 1

No matter what, it will cost 174.20 per month for insurance and payment.  Whether you drive the car 1 mile, or 1000 miles, you will pay 174.20 per month for this.  That makes 174.20 your "constant" figure.  Miles driven can vary month to month, so this will be your variable figure (or calculated amount).

We know that "x" represents miles, and it costs .29 "per mile".  So we know that part will be .29x ( 29 cents multiplied by who knows how many miles).  And because we know we're going to pay 174.20 every month no matter what, we add this to whatever our costs per mile total is ( this makes it our + b ).

So the answer would be y = .29x + 174.20