Question

Find the equation of the line perpendicular to the line \[ 7x - 5y = 11 \] and passing through the point \( (7, -9) \).

• A. \( 5x + 7y + 28 = 0 \)
• B. \( 5x + 7y - 28 = 0 \)
• C. \( 5x + 7y + 38 = 0 \)
• D. \( 5x + 7y - 38 = 0 \)
• E. \( 5x - 7y + 28 = 0 \)

Hint:

To find the perpendicular line, take the negative reciprocal of the given line's slope.

Answer 1

The Correct Option is A

The given line equation is: \[ 7x - 5y = 11 \] Slope of the given line: \[ m_1 = \frac{7}{5} \] Since perpendicular slopes are negative reciprocals: \[ m_2 = -\frac{5}{7} \] Using the point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting \( (7, -9) \): \[ y + 9 = -\frac{5}{7} (x - 7) \] Multiplying both sides by 7: \[ 7(y + 9) = -5(x - 7) \] \[ 7y + 63 = -5x + 35 \] \[ 5x + 7y + 28 = 0 \] Final Answer: \[ \boxed{5x + 7y + 28 = 0} \]