The expression
which best fit exists in the Linear model.
<h3>
How to estimate the linear model?</h3>
Given: Monthly Rate = $20
Number of customers = 5000
If there exists a decrease of $1 in the monthly rate, the number of customers increases by 500.
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19
Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18
Number of customers = 5500 + 500 = 6000
Linear change in the number of customers whenever there exists a decrease in the monthly rate.
We have 2 pairs of values here,
x = 20, y = 5000
x = 19, y = 5500
The equation in slope-intercept form: y = mx + c
The slope of a function: ![$&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\](https://tex.z-dn.net/?f=%24%26m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%20%5C%5C)
![$&m=\frac{5500-5000}{19-20} \\](https://tex.z-dn.net/?f=%24%26m%3D%5Cfrac%7B5500-5000%7D%7B19-20%7D%20%5C%5C)
![$&\Rightarrow-500](https://tex.z-dn.net/?f=%24%26%5CRightarrow-500)
So, the equation is y = -500x + c
Putting x = 20, y = 5000:
![$&5000=-500 \times 20+c \\](https://tex.z-dn.net/?f=%24%265000%3D-500%20%5Ctimes%2020%2Bc%20%5C%5C)
![$&\Rightarrow c=5000+10000=15000 \\](https://tex.z-dn.net/?f=%24%26%5CRightarrow%20c%3D5000%2B10000%3D15000%20%5C%5C)
![$&\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000](https://tex.z-dn.net/?f=%24%26%5CRightarrow%20%5Cmathbf%7By%7D%3D-500%20%5Cmathbf%7Bx%7D%2B15000)
Whether (18,6000) satisfies it.
Putting x = 18
![$-500 \times 18+15000=-9000+15000=6000](https://tex.z-dn.net/?f=%24-500%20%5Ctimes%2018%2B15000%3D-9000%2B15000%3D6000)
Therefore, the expression
which best fits exist Linear model.
To learn more about the linear model refer to:
brainly.com/question/6110794
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