Question

An account executive receives a base salary plus a commission. On $20,000 in monthly sales, an account executive would receive compensation of $1,900. On $40,000 in monthly sales, an account executive would receive compensation of $2,700. Determine a linear function that yields the compensation y (in dollars) of a sales executive for x dollars in monthly sales.

Answer 1

The equation is y = 0.04x + 1100

Explanation:

The computation of the linear function is as follows

Here the slope-intercept form could be used i.e.

y = mx + b

where,

x = monthly sales

and, y = compensation

x_1 y_1 x_2 y_2

($20,000, $1,900) ($40,000, $2,700)

Now

m = (y_2 - y_1) ÷ (x_2 - x_1)

= ($2,700 - $1,900) ÷ ($40,000 - $20,000)

= ($800) ÷ ($20,000)

= 2 ÷50

= 4%

Now for determining the b one of the ordered pairs could be chosen and then placing it into the above equation

y = mx+b.

Let use (x_2, y_2) or ($40,000, $2,700)

y = mx+b

$2,700 = 0.04 ($40,000)+b

$2,700 = $1,600 + b

b = $1,100

So,

The equation is y = 0.04x + 1100