To determine the relationship between the amount of money the painter earns and the number of rooms painted, let's break down the problem:
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The painter spends $60 on supplies. This means that the initial (fixed) cost the painter incurs before earning any money is $60.
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The painter charges $20 for each room painted. Therefore, if the painter paints \( x \) rooms, the amount earned from painting can be calculated as \( 20x \).
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The total amount earned (which is the revenue from painting minus the initial cost) can be expressed as: \[ \text{Total Earnings} = 20x - 60 \] Here, \(20x\) is the income from painting \( x \) rooms, and we subtract the $60 cost for supplies.
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The formula \( 20x - 60 \) indicates that when \( x = 0 \) (no rooms painted), the painter's earnings are \(-60\). This is where the line starts on the y-axis.
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As \( x \) increases (more rooms painted), the earnings will increase by $20 for each additional room.
By plotting this equation, we see:
- The graph starts from the point \( (0, -60) \) since the painter incurs a fixed cost of $60 before earning anything.
- When the painter paints 3 rooms, the earnings will be: \[ 20 \times 3 - 60 = 60 - 60 = 0 \]
So the painter earns $0 after painting 3 rooms.
Given this analysis, the correct graph representation would be the one that starts at \( (0, -60) \) and passes through \( (3, 0) \):
The correct answer is: a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 60 through the point 3 comma 0.