Question

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

Answer 1

Answer:

$y=100-20x$

Step-by-step 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

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$m=\frac{80-100}{1-0}$

$m=-20$

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 $y=100-20x$