Question

Alex earns $20.00 an hour doing contract work online and $10.00 an hour at his warehouse job. The monthly payment for his truck is $250.00 and his part of the rent is $750. Alex needs to make at least enough to cover these bills each month.

Which of the following graphs represents this situation?


O.
P.

Q.
R.

Answer 1

To determine how to graph Alex's earnings and expenses, let’s break down the situation into an equation.

1. **Income Calculation**:
- Let \( x \) be the number of hours Alex works on contract work at $20.00 per hour.
- Let \( y \) be the number of hours he works at the warehouse at $10.00 per hour.
- His total income can be represented as:
\[
I = 20x + 10y
\]

2. **Expense Calculation**:
- Alex's total monthly bills (expenses) include his truck payment and rent:
\[
E = 250 + 750 = 1000
\]

3. **Sustainable Earnings**:
- Alex needs to make at least enough money to cover his expenses:
\[
20x + 10y \geq 1000
\]

4. **Rearranging the Equation**:
- We can rearrange this equation to represent it in the slope-intercept form:
\[
20x + 10y = 1000
\]
- Dividing all terms by 10:
\[
2x + y = 100
\]
- Rearranging gives us:
\[
y = -2x + 100
\]
- Here, the slope is -2 (indicating that as Alex works more contract hours, his income from the warehouse decreases) and the y-intercept is 100.

### Plotting:
- The graph should have a straight line with a negative slope, starting at y=100 when \( x=0 \) (meaning if he works 0 hours of contract work, he needs to work enough hours at the warehouse to make 1000, which means 100 hours at $10/hour).

### Answer:
To choose the appropriate graph (O, P, Q, R), you need to look for:
- A line with a negative slope,
- An intercept at (0, 100).

Unfortunately, without the graphs to look at, I can't definitively choose the graph, but this explanation should help you identify which graph represents this situation! If you can provide descriptions or features of graphs O, P, Q, and R, I can help you more specifically!