To determine which linear equation represents the data points provided, we can analyze each equation option by looking for one that fits all the points (-5,0), (0,5), and (2,7).
The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Testing Each Option:
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Option 1: \( y = \frac{1}{5}x + 5 \)
- For \( x = -5 \): \( y = \frac{1}{5}(-5) + 5 = -1 + 5 = 4 \) (wrong)
- For \( x = 0 \): \( y = 5 \) (correct)
- For \( x = 2 \): \( y = \frac{1}{5}(2) + 5 = \frac{2}{5} + 5 = 5.4 \) (wrong)
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Option 2: \( y = -x + 5 \)
- For \( x = -5 \): \( y = -(-5) + 5 = 5 + 5 = 10 \) (wrong)
- For \( x = 0 \): \( y = 5 \) (correct)
- For \( x = 2 \): \( y = -2 + 5 = 3 \) (wrong)
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Option 3: \( y = x + 5 \)
- For \( x = -5 \): \( y = -5 + 5 = 0 \) (correct)
- For \( x = 0 \): \( y = 0 + 5 = 5 \) (correct)
- For \( x = 2 \): \( y = 2 + 5 = 7 \) (correct)
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Option 4: \( y = -5x + 5 \)
- For \( x = -5 \): \( y = -5(-5) + 5 = 25 + 5 = 30 \) (wrong)
- For \( x = 0 \): \( y = 5 \) (correct)
- For \( x = 2 \): \( y = -5(2) + 5 = -10 + 5 = -5 \) (wrong)
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Conclusion: The only equation that correctly represents all three points is option 3:
\[ y = x + 5 \]