Find the solution to the system: x/32 − y/2 =−4 x/2 + y/4 =−2

Part A. In order to know the function, the first step is to plot the points for both cars. In the picture, this is represented by the blue and orange lines for Car 1 and Car 2, respectively. When you connect the dots, it forms a smooth line. Therefore, both functions are linear.

Part B. In this case, you have to find the m and b for the standard form of a linear equation, y=mx + b, wherein m is the slope and b is the y-intercept. But, you can use MS Excel to make a trendline and know the linear equation from it through linear regression. The equation for car 1 is y=-6000x+38000 and that for car 2 is y=-4481.6x+36661.

Part C. In the formulated equations in Part B, we use this to know the value of y by replacing x = 5 years.

Car 1:
y = -6000(5)+38000 = $8,000
Car 2:
y=-4481.6(5)+36661 = $14,253

There is a significant difference, obviously. For Car 1, the value dropped from $20,000 to $8000 in just a year. For Car 2, the value dropped from $23,336.75 to $14,253 in just a year.