To determine which equations may represent the given graph, we need to analyze each equation to find its slope and y-intercept, and then compare those characteristics to the graph.
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y = -2/3x + 5
- Slope: -2/3
- Y-intercept: 5
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2x + 3y = 15
- Rearranging to slope-intercept form (y = mx + b):
- 3y = -2x + 15
- y = -2/3x + 5
- Slope: -2/3
- Y-intercept: 5
- Rearranging to slope-intercept form (y = mx + b):
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y = 5x + 8
- Slope: 5
- Y-intercept: 8
-
-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
To identify which graphs could match the described graph, we check each one for matching slopes and y-intercepts with the graph data. If the slopes and y-intercepts match visually with the graph provided, then these equations would apply.
Based on the analysis above:
- y = -2/3x + 5 and 2x + 3y = 15 represent the same line and could both represent part of the graph.
- The other three equations have different slopes and y-intercepts that do not match the properties of the first two lines.
Therefore, the correct responses are:
- y = -2/3x + 5
- 2x + 3y = 15
1 answer