To match the graphs with their corresponding equations, we can first rewrite each equation in slope-intercept form (y = mx + b) and then identify their characteristics (like slope and intercepts).
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Equation: 7x – 7y = –49 \[ -7y = -7x - 49 \ y = x + 7 \]
- Slope: 1 (positive), y-intercept: 7
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Equation: –7x + 7y = –49 \[ 7y = 7x - 49 \ y = x - 7 \]
- Slope: 1 (positive), y-intercept: -7
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Equation: 7x + 7y = 0 \[ 7y = -7x \ y = -x \]
- Slope: -1 (negative), y-intercept: 0 (origin)
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Equation: 7x + 7y = 49 \[ 7y = -7x + 49 \ y = -x + 7 \]
- Slope: -1 (negative), y-intercept: 7
Now, we can summarize the characteristics of these lines:
- The first equation has a positive slope and a positive y-intercept (1, 7).
- The second equation has a positive slope and a negative y-intercept (1, -7).
- The third equation is a negative slope line going through the origin (y = -x).
- The fourth equation is a negative slope line with a positive y-intercept (0, 7).
Using this information, you can now match the graphs visually based on their slopes and intercepts.