Question 1132077
examination of the point pairs for each car yields the following:


the value for car 1 is depreciating by 3280 dollars every 25000 miles.
the value for car 2 is depreciating by 2570 dollars every 25000 miles.


the change in the value of y divided by the change in the value of x for car 1 is therefore equal to -3280 / 25000 = -.1312.


the change in the value of y divided by the change in the value of x for car 2 is therefore equal to -2570 / 25000 = -.1028.


y is the value of the car.
x is the number of miles the car has been driven


the equation for the value of each car is y = mx + b
m is the slope which is the change in the value of y divided by the change in the value of x.
b is the y-intercept.


the equation for car 1 becomes y = -.1312 * x + 26240


the equation for car 2 becomes y = -.1028 * x + 22946


i'm assuming you know how to derive the value of the y-intercept so i won't get into it here.


the cars will have the same value when the equation for car 1 is equal to the equation for car 2.


this occurs when -.1312 * x + 26240 = -.2018 * x + 22946


solve for x in this equation to get x = 3294 /.0284 = 115985.9155.


round this to nearest 1000 to get x = 116000.


that's selection B.


a graph of both equations and their intersection is shown below:


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