To determine which equations could represent the graph, we need to assess the slope and y-intercept of each equation and compare them with the characteristics of the given graph.
Here are the equations reviewed:
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y = -2/3x + 5: This has a negative slope (-2/3) and a y-intercept of 5.
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2x + 3y = 15: Rearranging into slope-intercept form (y = mx + b): \[ 3y = -2x + 15 \implies y = -\frac{2}{3}x + 5 \] This has the same slope and intercept as the first equation, so it is equivalent.
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-3x + 2y = 5: Rearranging into slope-intercept form: \[ 2y = 3x + 5 \implies y = \frac{3}{2}x + \frac{5}{2} \] This has a positive slope (3/2) and is unlikely to match with a graph with a negative slope.
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y = 5x - 2: This has a positive slope (5) and a negative y-intercept (-2). This will not match with any negative slope graph.
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y = 5x + 8: This also has a positive slope (5) and a positive y-intercept (8), which again does not match with any negative slope graph.
Based on this analysis:
- The equations that could represent the graph, assuming it has a negative slope and an intercept of 5, are:
- y = -2/3x + 5
- 2x + 3y = 15
The equations that do not match are:
- -3x + 2y = 5
- y = 5x - 2
- y = 5x + 8
Final answer: y = -2/3x + 5 and 2x + 3y = 15.