Solve the equation

Question

Sales(x) Monthly pay(y)

january $100,000. $3,750

february $ 200,000 $5,750

You are paid a monthly salary plus commission at your sales job. Using data from two months, find the monthly salary (y-intercept) and commission rate (slope)

Answer 1

You have two sets of coordinates and can use the formula below to find the slope m

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) = (100,000, 3,750)

(x₂, y₂) = (200,000, 5,750)

m =.02 or 1/50 this is 2%

You can use the slope intercept form and a set of the coordinates to calculate b. I used the coordinates for January below.

y = mx + b

3750 = .02(100000) + b

3750 =2000 + b

Subtract 2000 from both sides of the equation to get b

3750 - 2000 = b

1750 = b

y = .02(x) + 1750

The commission rate is 2% and the monthly salary is $1,750

You can check by plugging x from the second set of coordinates, the ones for February, into the slope intercept form above to see if it gives the y value

y = .02(200,000) + 1750

y = 4000 + 1750

y = 5750

I hope you find this useful if you have any questions please send me a message.