To determine which equations could represent the graph, we'd typically analyze the slopes and intercepts of the equations provided. However, since the graph itself is not visible in this context, I'll explain how you can identify the correct equations based on the typical characteristics of lines.
- Slope: Examine the coefficients of \(x\) (for example, in \(y = mx + b\), \(m\) is the slope).
- Y-Intercept: Look at the constant term (for \(y = mx + b\), \(b\) is the y-intercept) and see where the graph intersects the y-axis.
- Standard Form: For equations in the form \(Ax + By = C\), you can convert them to slope-intercept form \(y = mx + b\) by isolating \(y\).
Let's analyze the equations provided:
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\(-3x + 2y = 5\):
- Rearranging gives \(2y = 3x + 5\), or \(y = \frac{3}{2}x + \frac{5}{2}\). Slope is \(\frac{3}{2}\).
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\(2x + 3y = 15\):
- Rearranging gives \(3y = -2x + 15\), or \(y = -\frac{2}{3}x + 5\). Slope is \(-\frac{2}{3}\).
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\(y = -\frac{2}{3}x + 5\):
- This slope is also \(-\frac{2}{3}\) and has a y-intercept of 5.
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\(y = 5x + 8\):
- This slope is 5, much steeper.
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\(y = 5x - 2\):
- This slope is also 5, and it has a different y-intercept than the previous equation.
Based on the characteristics of these equations, if you have determined that the graph has a slope of \(-\frac{2}{3}\) and a y-intercept of 5, both \(2x + 3y = 15\) and \(y = -\frac{2}{3}x + 5\) would apply. If it doesn't match those slopes and intercepts, then other options may not apply.
In summary, without the graph for visual confirmation, the possible answers would be:
- \(2x + 3y = 15\)
- \(y = -\frac{2}{3}x + 5\)
You might also need to assess the graph to see if the other slopes or intercepts match.
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