Create a linear function that yields the compensation (y) of a sales executive for a given amount of monthly sales (x).

Question

An account executive receives a base salary plus a commission. On $50,000 in monthly sales, an account executive would receive compensation of $3200. On $60,000 in monthly sales, an account executive would receive compensation of $3600. Determine a linear function that yields the compensation y of a sales executive for a given amount of monthly sales x.

Answer 1

We will use slope intercept form: y=mx+b

X and y are provided in the problem: x = monthly sales and y = compensation

We will have to find m (Slope), which in this problem represents the commission percentage, and b (y-intercept), which represents the the base salary.

x₁ y₁ x₂ y₂

(50000, 3200) (60000, 3600)

m = (y₂ - y₁) / (x₂ - x₁)

m = (3600 - 3200) / (60000 - 50000)

m = 400 / 10000 --> 4/100 (4%)

so m = 4% (which can be written as 0.04 or 4/100)

To find b, we have to take one of our ordered pairs [ (50000, 3200) or (60000, 3600) ] and plug it into the equation, y=mx+b.

Let's use (x₂, y₂) or (60000, 3600)

y = mx+b

3600 = 0.04(60000)+b

3600 = 2400+b

1200 = b

so b (the base salary) is = 1200

The equation is y = 0.04x + 1200