To determine which equations represent the given graph, we would typically need to analyze the graph itself. However, as we do not have the visual, we can evaluate each equation based on its general characteristics.
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y = 5x + 8: This is a line with a slope of 5.
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y = 5x - 2: This is also a line with a slope of 5, but with a different y-intercept.
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-3x + 2y = 5: Rearranging this gives \(2y = 3x + 5\) or \(y = \frac{3}{2}x + \frac{5}{2}\), indicating a line with a slope of \(\frac{3}{2}\).
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y = -\frac{2}{3}x + 5: This is a line with a slope of -\(\frac{2}{3}\).
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2x + 3y = 15: Rearranging gives \(3y = -2x + 15\) or \(y = -\frac{2}{3}x + 5\), indicating a line with a slope of -\(\frac{2}{3}\).
If you can derive the slope and y-intercept from the graph and compare it with these equations, you can determine which equations apply. Due to the absence of a graph, it's not possible to definitively state which equations are valid responses.
If the graph has a slope of 5, then y = 5x + 8 and y = 5x - 2 could be valid. If the slope is negative and equals -2/3, the equations y = -\frac{2}{3}x + 5 and 2x + 3y = 15 would be valid.
If you can provide the characteristics of the graph, I can help narrow it down further!
1 answer