Question

Write an equation in y = mx + b for the situation. A sales associate is given a $500 hiring bonus with a new job. She earns an average commission of $250 dollars per week.

a. y = 500x + 250
b. y = 250x + 500
c. y = 500x - 250
d. y = 250x - 500

Answer 1

The correct linear equation for a scenario where a sales associate earns a $500 bonus and a $250 commission per week is y = 250x + 500, where y is the total earnings and x is the number of weeks.

Step-by-step explanation:

The situation described involves a sales associate who is given a one-time hiring bonus and then earns a weekly commission. To represent this scenario with a linear equation in the form y = mx + b, let y represent the total earnings of the sales associate after x weeks, m represent the commission earned per week, and b represent the one-time hiring bonus.

The sales associate receives a $500 hiring bonus, which is the y-intercept (b), because this is the amount earned at the start, before any weeks of commission. The associate then earns $250 per week, which is the slope of the line (m), because for each week that passes, the earnings increase by this amount. Therefore, the correct linear equation for the given situation is y = 250x + 500, which means for every week (x), the total earnings (y) increase by $250 plus the initial hiring bonus of $500.