To determine how to graph Alex's earnings and expenses, let’s break down the situation into an equation.
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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: \[ I = 20x + 10y \]
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Expense Calculation:
- Alex's total monthly bills (expenses) include his truck payment and rent: \[ E = 250 + 750 = 1000 \]
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Sustainable Earnings:
- Alex needs to make at least enough money to cover his expenses: \[ 20x + 10y \geq 1000 \]
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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!
1 answer