Question

Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.

• A. \( \frac{4}{3} \)
• B. \( -\frac{4}{3} \)
• C. \( \frac{3}{4} \)
• D. \( -\frac{3}{4} \)

Hint:

To find the slope of a line perpendicular to a given line, compute the negative reciprocal of the original line’s slope.

Answer 1

The Correct Option is A

For the line \( 3x + 4y - 12 = 0 \), rewrite in slope-intercept form \( y = mx + c \): \[ 4y = -3x + 12 \implies y = -\frac{3}{4}x + 3 \] The slope of the given line is \( m = -\frac{3}{4} \). 
The slope of a line perpendicular to it is the negative reciprocal: \[ m_{\text{perpendicular}} = -\frac{1}{-\frac{3}{4}} = \frac{4}{3} \] Thus, the slope is: \[ \boxed{\frac{4}{3}} \]