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Sagot :
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:
[tex]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[/tex]
Therefore the value of the computer decreases by $800 per year.
Find out more at: https://brainly.com/question/13911928
A linear relationship will always decrease or increase at a constant and uniform rate.
- The linear equation is [tex]\mathbf{y = -600x +3200}[/tex]
- 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
[tex]\mathbf{(x,y) = (0,3200) (2,2000)}[/tex]
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{2000 - 3200}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{- 1200}{2}}[/tex]
Divide
[tex]\mathbf{m = - 600}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x -x_1) +y_1}[/tex]
So, we have:
[tex]\mathbf{y = -600(x -0) +3200}[/tex]
[tex]\mathbf{y = -600x +3200}[/tex]
Hence, the linear equation is [tex]\mathbf{y = -600x +3200}[/tex]
(b) The estimated value in 2022
In 2022, x = 4
So, we substitute 4 for x in the linear equation
[tex]\mathbf{y = -600x +3200}[/tex]
[tex]\mathbf{y = -600 \times 4 +3200}[/tex]
[tex]\mathbf{y = 800}[/tex]
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
[tex]\mathbf{y = -600x +3200}[/tex]
[tex]\mathbf{y = -600 \times 6 +3200}[/tex]
[tex]\mathbf{y = -400}[/tex]
Hence, the value in 2024 is -$400
This value does not make sense, because the value cannot be negative
Read more about linear equations at:
https://brainly.com/question/14323743
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