To determine which equations could represent the graph, we need to consider the slope and y-intercept of each line represented by the equations. Without a visual representation of the graph, I'll describe how to analyze the equations provided:
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y = 5x + 8
- Slope: 5, Y-intercept: 8
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y = -2/3x + 5
- Slope: -2/3, Y-intercept: 5
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2x + 3y = 15
- Rearranging to the slope-intercept form (y = mx + b):
- 3y = -2x + 15
- y = -2/3x + 5 (Slope: -2/3, Y-intercept: 5)
- Rearranging to the slope-intercept form (y = mx + b):
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-3x + 2y = 5
- Rearranging to slope-intercept form:
- 2y = 3x + 5
- y = (3/2)x + 5/2 (Slope: 3/2, Y-intercept: 5/2)
- Rearranging to slope-intercept form:
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y = 5x - 2
- Slope: 5, Y-intercept: -2
Now, to identify which equations apply to the graph, you would compare their slopes and y-intercepts with the characteristics of the graph you are examining.
- If the graph shows a line with a slope of 5, then the equations y = 5x + 8 and y = 5x - 2 would apply.
- If the graph shows a line with a slope of -2/3, then the equations y = -2/3x + 5 and 2x + 3y = 15 would apply.
- If the graph shows a line with a slope of 3/2, then -3x + 2y = 5 would apply.
So you would select the equations based on the visible slope and y-intercept on the graph.
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