Respuesta :
The expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fit exists in the Linear model.
How to estimate the linear model?
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 = $18
Number of customers = 5500 + 500 = 6000
Linear change in the number of customers whenever there exists a decrease in the monthly rate.
We have 2 pairs of values here,
x = 20, y = 5000
x = 19, y = 5500
The equation in slope-intercept form: y = mx + c
The slope of a function: [tex]${data-answer}amp;m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]
[tex]${data-answer}amp;m=\frac{5500-5000}{19-20} \\[/tex]
[tex]${data-answer}amp;\Rightarrow-500[/tex]
So, the equation is y = -500x + c
Putting x = 20, y = 5000:
[tex]${data-answer}amp;5000=-500 \times 20+c \\[/tex]
[tex]${data-answer}amp;\Rightarrow c=5000+10000=15000 \\[/tex]
[tex]${data-answer}amp;\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000[/tex]
Whether (18,6000) satisfies it.
Putting x = 18
[tex]$-500 \times 18+15000=-9000+15000=6000[/tex]
Therefore, the expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fits exist Linear model.
To learn more about the linear model refer to:
https://brainly.com/question/6110794
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