Question

Question
The value of a computer y, depreciates, or decreases as time passes. A computer was purchased for $3200 in 2018. In
2020 the computer was worth $2000. Assume the relationship between number of years after 2018 x, and value of
computer, y is linear.

Answer 1

The value of the computer decreases by $800 per year.

A linear equation is given by:

y = mx + b

where y, x are variables, m is the rate of change, b is the initial vale of y (y intercept).

Let y represent the cost of the computer and x represent the years after 2018.

A computer was purchased for $3200 in 2018. It is represented by the point (0, 3200). Also, in  2020 the computer was worth $2000, it is represented by the point (2, 2000). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3200=\frac{2000-3200}{2-0}(x-0)\\\\y-3200=-800x\\\\y=-800x+3200$

Therefore the value of the computer decreases by $800 per year.

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Answer 2

A linear relationship will always decrease or increase at a constant and uniform rate.

• The linear equation is $\mathbf{y = -600x +3200}$
• The estimated value in 2022 is $800
• The estimated value in 2024 is -$400, and it does not make sense

Part 1

(a) The linear equation

In 2018, the value is $3200

In 2020, the value is $2000

Let the number of years since 2018 be x, and the value be y

So, we have the following representation

$\mathbf{(x,y) = (0,3200) (2,2000)}$

Start by calculating the slope (m)

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

So, we have:

$\mathbf{m = \frac{2000 - 3200}{2 - 0}}$

$\mathbf{m = \frac{- 1200}{2}}$

Divide

$\mathbf{m = - 600}$

The equation is then calculated as:

$\mathbf{y = m(x -x_1) +y_1}$

So, we have:

$\mathbf{y = -600(x -0) +3200}$

$\mathbf{y = -600x +3200}$

Hence, the linear equation is $\mathbf{y = -600x +3200}$

(b) The estimated value in 2022

In 2022, x = 4

So, we substitute 4 for x in the linear equation

$\mathbf{y = -600x +3200}$

$\mathbf{y = -600 \times 4 +3200}$

$\mathbf{y = 800}$

Hence, the value in 2022 is $800

Part 2

The estimated value in 2024

In 2024, x = 6

So, we substitute 6 for x in the linear equation

$\mathbf{y = -600x +3200}$

$\mathbf{y = -600 \times 6 +3200}$

$\mathbf{y = -400}$

Hence, the value in 2024 is -$400

This value does not make sense, because the value cannot be negative

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