To determine if the two lines are parallel, we need to compare their slopes. Two lines are parallel if they have the same slope.
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Find the slope of the first line: The first line is given in slope-intercept form \( y = mx + b \): \[ y = \frac{3}{7}x + 11 \] Here, the slope \( m_1 \) is \( \frac{3}{7} \).
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Convert the second line to slope-intercept form: The second line is given as: \[ -3x + 7y = 13 \] We can rearrange this to solve for \( y \): \[ 7y = 3x + 13 \] \[ y = \frac{3}{7}x + \frac{13}{7} \] Here, the slope \( m_2 \) is also \( \frac{3}{7} \).
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Compare the slopes: Since both lines have the same slope: \[ m_1 = \frac{3}{7} \quad \text{and} \quad m_2 = \frac{3}{7} \]
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Conclusion: Yes, the graphs of the lines in the pair are parallel because they have the same slope of \( \frac{3}{7} \).
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