Answer:
a. y-intercept = 23350 and x-intercept = 13
b. ![m = -\frac{23350}{13}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B23350%7D%7B13%7D)
c. ![y = -\frac{23350}{13}x + 23350](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B23350%7D%7B13%7Dx%20%2B%2023350)
Step-by-step explanation:
Given
![Years = 13](https://tex.z-dn.net/?f=Years%20%3D%2013)
![Total\ depreciation = \$23350](https://tex.z-dn.net/?f=Total%5C%20depreciation%20%3D%20%5C%2423350)
Solving (a): The x and y intercepts
The y intercept is the initial depreciation value
i.e. when x = 0
This value is the value of the car when it was initially purchased.
Hence, the y-intercept = 23350
The x intercept is the year it takes to finish depreciating
i.e. when y = 0
From the question, we understand that it takes 13 years for the car to totally get depreciated.
Hence, the x-intercept = 13
Solving (b): The slope
The slope (m) is the rate of depreciation per year
This is calculated by dividing the total depreciation by the duration.
So:
![m = \frac{23350}{13}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B23350%7D%7B13%7D)
Because it is depreciation, it means the slope represents a deduction.
So,
![m = -\frac{23350}{13}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B23350%7D%7B13%7D)
Solving (c): The straight line equation
The general format of an equation is:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where
![m = slope](https://tex.z-dn.net/?f=m%20%3D%20slope)
![b = y\ intercept](https://tex.z-dn.net/?f=b%20%3D%20y%5C%20intercept)
In (a), we have that:
![y\ intercept = 23350](https://tex.z-dn.net/?f=y%5C%20intercept%20%3D%2023350)
In (b), we have that:
![Slope\ (m) = -\frac{23350}{13}](https://tex.z-dn.net/?f=Slope%5C%20%28m%29%20%3D%20-%5Cfrac%7B23350%7D%7B13%7D)
Substitute these values in ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![y = -\frac{23350}{13}x + 23350](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B23350%7D%7B13%7Dx%20%2B%2023350)
<em>Hence, the depreciation equation is: </em>
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