Suppose you buy a brand new car for $25,000. The car's value depreciates each year by $2,000. How much is the car worth after 1 year? How much is the car worth after 2 years? Write a slope intercept equation that expresses the value of the car related to its age. Use x to represent the age of the car.
1 year 25000 - 1*2000 = 23000
2 years 25000 - 2*2000 = 21000
v = -2000 x + 25000
To find the worth of the car after 1 year, you need to subtract the depreciation from the original price. The depreciation is given as $2,000 per year, so after 1 year, the car's value decreases by $2,000.
The worth of the car after 1 year can be calculated as follows:
Original price - Depreciation = $25,000 - $2,000 = $23,000.
Hence, the car is worth $23,000 after 1 year.
To find the worth of the car after 2 years, you need to subtract another $2,000 worth of depreciation from the value after 1 year.
The worth of the car after 2 years can be calculated as follows:
Value after 1 year - Depreciation = $23,000 - $2,000 = $21,000.
So, the car is worth $21,000 after 2 years.
To write a slope-intercept equation that expresses the value of the car related to its age, we can use the following formula:
Value = Original price - (Depreciation x Age)
Using x to represent the age of the car:
Value = $25,000 - ($2,000 x x)
Simplifying the equation, we have:
Value = $25,000 - $2,000x
This is the slope-intercept equation that represents the value of the car related to its age.
To find the car's worth after 1 year, subtract the depreciation amount of $2,000 from the initial value of $25,000:
$25,000 - $2,000 = $23,000
Therefore, the car is worth $23,000 after 1 year.
To find the car's worth after 2 years, we need to subtract the depreciation amount twice since 2 years have passed:
$25,000 - 2 * $2,000 = $25,000 - $4,000 = $21,000
Therefore, the car is worth $21,000 after 2 years.
To express the value of the car in terms of its age using a slope-intercept equation, we can represent the initial value of the car as the y-intercept, and the depreciation amount each year as the slope.
y = mx + b
where,
y represents the value of the car,
x represents the age of the car,
m represents the slope, which is the depreciation amount per year, and
b represents the y-intercept, which is the initial value of the car.
In this case, the slope (m) would be -$2,000, and the y-intercept (b) would be $25,000, since that is the initial value of the car.
So, the equation that expresses the value of the car (y) as a function of its age (x) would be:
y = -$2,000x + $25,000