Question

Alex bought a new car for his daughter. He knows the value of the car will decrease at a constant rate. After 3 years, the value of the car is $15,000. After 5 years, the value of the car of $11,000. Write and solve a linear equation to find the value of the car after 8 years. (Drop down and select)

y-______=______(x-____)
The value of the car after 8 years will be ______.

Answer 1

To find the value of the car after 8 years, we can use the slope and y-intercept to write a linear equation. The equation is y = -1000x + 18000, where x is the number of years and y is the value of the car. Substituting x = 8 into the equation, we find that the value of the car after 8 years will be $10,000.

Step-by-step explanation:

To write a linear equation, we need to determine the slope and y-intercept. We can use the given values to find the slope using the formula (change in y) / (change in x).

Using the values (3, 15000) and (5, 11000), we can calculate the slope as (11000-15000) / (5-3) = -2000 / 2 = -1000.

Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1). Substituting the values (3, 15000) and the slope (-1000), we get the equation y - 15000 = -1000(x - 3). Solving for y, we find y = -1000x + 18000.

To find the value of the car after 8 years, we substitute x = 8 into the equation and solve for y. y = -1000(8) + 18000 = -8000 + 18000 = 10000. Therefore, the value of the car after 8 years will be $10,000.