Question

1. jaylen got a job paying $9.50 an hour at the coffee shop. but 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: Determine the linear equation

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the \(y -\)intercept. Jaylen earns \( \$9.50\) per hour (\(m = 9.5\)) and has an initial “debt” (because he spent money) of \(b=- 70\). So the equation is \(y = 9.5x-70\).

Step2: Find the value for \(x = 35\)

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

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Answer:

a. The equation is \(y = 9.5x-70\).
d. When \(x = 35\), \(y=262.5\). So Jaylen netted \(\$262.50\) on his paycheck.