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The initial cost of an office fax machine is $100. After 1 year, its value becomes $80. Which is the correct linear depreciation model?

User Enjayy
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1 Answer

3 votes

Answer:


y=100-20x

Explanation:

Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).

We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).

Now we can find the slope of the line passing through those two points using the slope formula


m=(y_2-y_1)/(x_2-x_1)

where


m is the slope


(x_1,y_1) are the coordinates of the first point


(x_2,y_2) are the coordinates of the second point

Replacing values:


m=(80-100)/(1-0)


m=-20

Now, to complete our model we are using the point slope formula


y-y_1=m(x-x_1)

where


m is the slope


(x_1,y_1) are the coordinates of the first point

Replacing values:


y-100=-20(x-0)


y-100=-20x


y=-20x+100


y=100-20x

We can conclude that the correct linear depreciation model is
y=100-20x

User Stela
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9.0k points