Question

A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales.

a. Identify the Slope m _________
b. Identify the initial value b ________________
c. Write an equation that gives the weekly income y in terms of sales x ______________.
d. What is his weekly income if the sales were $600.00?

Answer 1

a. The slope m is 0.02

b. The initial value b is 250

c. y = 0.02x + 250

d. His weekly income is $262 if the sales were $600.00

Explanation:

the form of the linear equation is y = m x + b, where

• m is the slope (rate of change)

• b is the y-intercept (constant amount)

∵ A real estate sales agent receives a salary of $250 per week

→ This is a fixed amount every week

∴ b = 250

∵ They give a commission of 2% of sales

→ This value depends on the sales (rate of change)

∵ 2% = 2 ÷ 100 = 0.02

∴ m = 0.02

a. The slope m is 0.02

b. The initial value b is 250

∵ y represents the weekly income

∵ x represents the sales

∵ m = 0.02 and b = 250

∴ The equation is y = 0.02x + 250

c. y = 0.02x + 250

∵ The sales were $600.00

∴ x = 600

→ Substitute it in the equation to find y

∵ y = 0.02(600) + 250

∴ y = 12 + 250

∴ y = 262

d. His weekly income is $262 if the sales were $600.00