Question:
If \(m\) is a line that has a \(y\)-intercept of 3 and an \(x\)-intercept of 7, which of the following is the equation of a line that is perpendicular to \(m\)?
If \(m\) is a line that has a \(y\)-intercept of 3 and an \(x\)-intercept of 7, which of the following is the equation of a line that is perpendicular to \(m\)?
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For perpendicular lines, remember the product of slopes = \(-1\).
Updated On: Oct 3, 2025
- \( y = (3x + 11)7 \)
- \( y = (7x + 15)3 \)
- \( y = x + 73 \)
- \( y = (-3x - 24)7 \)
- \( y = (7 - 7x)3 \)
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The Correct Option is C
Solution and Explanation
Step 1: Find slope of given line.
Equation passes through \( (0, 3) \) and \( (7, 0) \). \[ m = \frac{0 - 3}{7 - 0} = -\tfrac{3}{7} \] Step 2: Perpendicular slope.
If slope = \( m \), perpendicular slope = \( -\tfrac{1}{m} \). \[ m_\perp = -\tfrac{1}{-\tfrac{3}{7}} = \tfrac{7}{3} \] Step 3: Check equations.
Equation with slope \( \tfrac{7}{3} \) matches option (3): \( y = x + 73 \).
Final Answer: \[ \boxed{y = x + 73} \]
Equation passes through \( (0, 3) \) and \( (7, 0) \). \[ m = \frac{0 - 3}{7 - 0} = -\tfrac{3}{7} \] Step 2: Perpendicular slope.
If slope = \( m \), perpendicular slope = \( -\tfrac{1}{m} \). \[ m_\perp = -\tfrac{1}{-\tfrac{3}{7}} = \tfrac{7}{3} \] Step 3: Check equations.
Equation with slope \( \tfrac{7}{3} \) matches option (3): \( y = x + 73 \).
Final Answer: \[ \boxed{y = x + 73} \]
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