The value of a car decreases at a constant rate. After 1 year the value of the car is $20,000. After 2 more yearsit is $14,000. Write an equation in slope-intercept that represents the value y (in dollars) of the car after x years.
http://www.jiskha.com/display.cgi?id=1477157306
i do not understand but i guess it is 68,000 years can you pls explain
To find the equation that represents the value y of the car after x years, we need to determine the slope and the y-intercept.
Given that the value of the car decreases at a constant rate, we can conclude that the slope of the line representing the car's value is constant. Let's use the information provided to determine the slope:
We know that after 1 year, the car's value is $20,000, and after 3 years (1 + 2), the car's value is $14,000.
The change in value is calculated by subtracting the initial value from the final value. Therefore, the change in value over 2 years is $14,000 - $20,000 = -$6,000.
The change in time (x) over the same period is 2 - 1 = 1 year.
The slope (m) is calculated by the change in value divided by the change in time:
m = (-$6,000) / (1) = -$6,000
So, the slope (m) of the line representing the car's value is -$6,000.
Now let's find the y-intercept.
Given that after 1 year, the car's value is $20,000, we can conclude that when x = 0 (representing the initial value), the car's value is $20,000.
So, the y-intercept (b) is $20,000.
Now that we have the slope and the y-intercept, we can write the equation in slope-intercept form (y = mx + b):
y = (-$6,000)x + $20,000
Therefore, the equation representing the value y (in dollars) of the car after x years is y = (-$6,000)x + $20,000.