a) We were told that relationship between the value of the car and its age is linear. This means that it can be represented with a linear equation such as
y = mx + c
y is the dependent variable and in this case, it is the value of the car, V
x is the independent variable and in this case, it is the age of the car, a
The above equation is the slope intercept form equation where
m represents slope
c represents y intercept
The formula for determining slope is expressed as:
m = (y2 - y1)/(x2 - x1)
We were told that a 5 year old car is worth 14000. This means that
When x1 = 5, y1 = 14000
Also, the same car is worth 11400 after 2 years. This means that the car is worth 11400 after 7 years. Thus,
when x2 = 7, y2 = 11400
Thus,
slope, m = (11400 - 14000)/(7 - 5) = - 2600/2
m = - 1300
We would find the y intercept, c by substituting m = - 1300, x = 5 and y = 14000 into the slope intercept equation. Thus,
14000 = - 1300 * 5 + c
14000 = - 6500 + c
c = 14000 + 6500
c = 20500
Thus, by substituting m = - 1300 and c = 20500 into the slope intercept equation, the linear equation representng this scenario is
y = - 1300x + 20500
By replacing with the given variables,
V = - 1300a + 20500
b) When the car was new, it means that a = 0. By substituting a = 0 into the equation, we have
V = - 1300 * 0 + 20500
V = 20500
The value of the car was $20500 when it was new
