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Math  /  Algebra

QuestionQuestion 2 Joe owns an auto-repair shop. He charges his customers an hourly rate for repairs. The relationship between his income and the amount of time he works is shown below.
Income vs. Time Worked
What is Joe's hourly rate? a $25\$ 25 hour b $75\$ 75 hour c $150\$ 150 hour d \$225/hour

Studdy Solution

STEP 1

What is this asking? How much money does Joe make every hour he works? Watch out! Make sure to read the graph carefully!

STEP 2

1. Find a Point
2. Calculate the Rate

STEP 3

Alright, let's **decode** this graph!
We need to find a point on the line to figure out how much Joe earns in a specific amount of time.

STEP 4

Look! The graph gives us a clear point: (1,75)(\textbf{1}, \textbf{75}).
This tells us that when Joe works 1\textbf{1} hour, he earns $75\$\textbf{75}.
How cool is that?!

STEP 5

Now, let's **calculate** Joe's hourly rate.
The hourly rate is simply how much money he makes per hour.

STEP 6

We know from our point (1,75)(\textbf{1}, \textbf{75}) that Joe earns $75\$\textbf{75} for every 1\textbf{1} hour he works.
So, to find his hourly rate, we can divide his earnings by the number of hours he worked:
Hourly Rate=EarningsTime Worked\text{Hourly Rate} = \frac{\text{Earnings}}{\text{Time Worked}}

STEP 7

Let's **plug in** our values:
Hourly Rate=$751 hour\text{Hourly Rate} = \frac{\$\textbf{75}}{\textbf{1} \text{ hour}}

STEP 8

And now, let's **calculate**!
Hourly Rate=$75/hour\text{Hourly Rate} = \$ \textbf{75}/\text{hour}

STEP 9

Joe's hourly rate is $75\$\textbf{75} per hour, which matches answer choice *b*.

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