Question

Elena and her husband Marc both drive to work. Elena's car has a current mileage (total distance driven) of 9,000 and she drives 22,000 miles more each year. Marc's car has a current mileage of 22,000 and he drives 22,000 miles more each year. Will the mileages for the two cars ever be equal? Explain.

(answer choices included)

Answer 1

If we make equations:
y-total mileage, x-years of driving
Elena: y=9000+22000*x
Marc: y=22000+22000*x
The general form of the linear function is: y=kx+n, where k represents the slope of the line relative to the x axis, and n tells us where the line will intersect the y axis.
This two functions have same k coefficient, so they have same slopes but different y-intercepts, so the lines do not intersect which means the mileage of two cars will never be equal.

Answer 2

The mileage of the two cars will never be equal. This is because Elena has less mileage on her car to begin with, and both Elena and Marc drive the same amount of miles every year. Marc's car will always have a higher mileage.