Question

1. jaylen got a job paying $9.50 an hour at the first week there he spent $70.00 on smoothies, mu 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.

Explanation:

Step1: Analyze the linear equation form

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. For the equation \(y = 9.5x-70\) (assuming a correction from the hand - written \(y = 4.5x + 70\) as \(9.5\) is more reasonable for an hourly wage situation, if the initial thought was wrong, the process is similar).

Step2: Identify the slope

The slope \(m = 9.5\). In the context of the situation, the slope represents the rate of change of the net - ted amount with respect to the number of hours worked. So, for each hour Jaylen works, his net - ted amount (after subtracting the \( \$70\) spent) increases by \( \$9.50\).

Step3: Identify the \(y\) - intercept

The \(y\) - intercept \(b=-70\). In the context of the situation, when \(x = 0\) (Jaylen has worked \(0\) hours), the value of \(y\) is \(-70\). This means that before he starts working (at \(0\) hours of work), he has a net - ted amount of \(-\$70\) (because he spent \( \$70\) on smoothies and macchiatos).

Answer:

The slope is \(9.5\), which means Jaylen earns \( \$9.50\) per hour. The \(y\) - intercept is \(-70\), which means Jaylen had a debt (or negative balance) of \( \$70\) before starting to work (due to his initial spending on smoothies and macchiatos).