The linear equation for both retailers are [tex]y =11.75x+4[/tex] and [tex]y =10.25x +16[/tex], respectively
What is a linear function?
The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope
A linear function is represented as:
[tex]y=mx+c[/tex]
Where
- m represents slope
- c represents the y-intercept
Linear Equation of Retailer 1
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{51 - 15.75}{4-1}[/tex]
[tex]m = \frac{35.25}{3}[/tex]
[tex]m = 11.75[/tex]
The linear equation is then calculated as:
[tex]y =m(x -x_1) + y_1[/tex]
So, we have:
[tex]y =11.75(x -1) + 15.75[/tex]
[tex]y =11.75x -11.75 + 15.75[/tex]
[tex]y =11.75x+4[/tex]
Linear Equation of Retailer 2
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{57 - 26.25}{4-1}[/tex]
[tex]m = \frac{30.75}{3}[/tex]
[tex]m = 10.25[/tex]
The linear equation is then calculated as:
[tex]y =m(x -x_1) + y_1[/tex]
So, we have:
[tex]y =10.25(x -1) + 26.25[/tex]
[tex]y =10.25x -10.25 + 26.25[/tex]
[tex]y =10.25x +16[/tex]
Hence, the linear equation for both retailers are [tex]y =11.75x+4[/tex] and [tex]y =10.25x +16[/tex], respectively
Read more about linear functions at:
https://brainly.com/question/14323743
