How would you express the monthly cost as a function?

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 miles and in June it cost her $460 to drive 800 miles.





How would you express the monthly cost C as a function of the distance driven d, assuming that a linear relation ship gives a suitable model? I had these kinds of math problems last year, but I can't remember quite how to do them.

How would you express the monthly cost as a function?
use your $ amt and distance like they were x,y and find slope intercept


(380-460)/(480-800) = -80/-320=1/4 = slope


C=1/4d+b


460=1/4(800)+b


b=260





C=1/4d+260
Reply:Consider the two points (400, 380) and (800, 460). Find the slope between them.





(460-380)/(800-460) = 1/5





Then, plug the slope and a point into point-slope formula:





y - y1 = m(x - x1)





y - 380 = (1/5)(x - 400)


y - 380 = (1/5)x - 8


y = (1/5)x + 372





So, C = 372 + (1/5)d
Reply:Write out the equation of a line





a = m*b + c,


where


a is cost in $


b is distance in miles


c is the fixed cost


m is the slope of the line





m = diffence in cost/difference in miles


= (460 - 380)/(800 - 380) = 0.25





Use on of the two given points to solve for c


$380 = 480*0.25 + c


c = 380 - 480*0.19 = $260
Reply:This is in the form of y=mx+c


For $380 distance covered 480 miles


for $ 480 distance covered 800 miles





so equations are


380=480m + c


460=800m + c





deduct first equation from second


80 = 320m


m = 80/320=1/4


equation for the problem is y=x/4+c
Reply:linear equation: y = mx + b


y being the cost, x being the miles driven.


b is the cost if she drove 0 miles.


your two sample points:


1. 380 = m(480) + b


2. 460 = m(800) + b





rearrange #1: b = 380 - m(480)


substitute for b in #2: 460 = m(800) + [380 - m(480)]


collect the like terms: 460 - 380 = m(800) - m(480)


factor out m and simplify: 80 = 120m


divide by the coefficient of m: 80/120 = m


simplify: 2/3 = m





using #1 again subsitute for m: 1. 380 = [2/3](480) + b


solve for b: 60 = b


substitute your results into the format y = mx + b:


y = 2/3x + 60