Answer:
Profit = $3100
Step-by-step explanation:
Since it is a LINEAR FUNCTION, we can take laws as the x-coordinate and profit as y-coordinate. Thus we have 2 points that we can write:
<u>Point 1</u>: (25,2000)
<u>Point 2</u>: (11, 600)
<em>With two points, we can find equation of the line passing through this two points by the equation:</em>
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
Where
and ![(x_2,y_2)=(11,600)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%3D%2811%2C600%29)
<em>Substituting the values, we have:</em>
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-2000=\frac{600-2000}{11-25}(x-25)\\y-2000=\frac{-1400}{-14}(x-25)\\y-2000=100(x-25)\\y=100x-100(25)+2000\\y=100x-2500+2000\\y=100x-500](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5Cy-2000%3D%5Cfrac%7B600-2000%7D%7B11-25%7D%28x-25%29%5C%5Cy-2000%3D%5Cfrac%7B-1400%7D%7B-14%7D%28x-25%29%5C%5Cy-2000%3D100%28x-25%29%5C%5Cy%3D100x-100%2825%29%2B2000%5C%5Cy%3D100x-2500%2B2000%5C%5Cy%3D100x-500)
<em>We need to find profit when 36 laws are services. Since x is laws, and y is profit, we plug in 36 into x and solve for y:</em>
![y=100x-500\\y=100(36)-500\\y=3100](https://tex.z-dn.net/?f=y%3D100x-500%5C%5Cy%3D100%2836%29-500%5C%5Cy%3D3100)
Profit is $3100