Question

1. jaylen got a job paying $9.50 an hour at the coffee shop, but the first week there he spent $70.00 on smoothies, muffins, and frozen macchiatos.

a. write an equation that represents the amount netted, y, given x number of hours worked.
b. graph the equation.
c. identify the slope and y - intercept of the graph. explain what each means in terms of the situation.
d. jaylen worked 35 hours this past week. what is the amount netted on his paycheck?

Explanation:

Step1: Analyze the relationship between hours worked and net amount

The amount earned from working \(x\) hours at a rate of \(\$9.50\) per hour is \(9.5x\). Since he spent \(\$70\), the net amount \(y\) is \(y = 9.5x-70\) (not \(y = 4.5x + 70\) as wrongly written in the problem statement).

Step2: For part c

The equation \(y=9.5x - 70\) is in the slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
The slope \(m = 9.5\). In the context of the problem, it means that for each additional hour Jaylen works, his net amount increases by \(\$9.50\).
The \(y\) - intercept \(b=-70\). In the context of the problem, it means that if Jaylen works \(0\) hours (\(x = 0\)), his net amount is \(-\$70\) (he has a debt or an expense of \(\$70\) with no income from the job).

Step3: For part d

Substitute \(x = 35\) into the correct equation \(y=9.5x-70\).

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Answer:

a. The correct equation is \(y = 9.5x-70\)
c. Slope \(m = 9.5\) (net amount increases by \(\$9.50\) per hour worked), \(y\) - intercept \(b=-70\) (net amount is \(-\$70\) when \(0\) hours worked)
d. \(\$262.50\)