Question

decide whether the pair of lines is parallel, perpendicular, or neither.
$3x + 4y = 1$
$4x - 3y = 2$

the lines are
a. parallel.
b. neither.
c. perpendicular.

Explanation:

Step1: Convert to slope-intercept form

For $3x + 4y = 1$:
$4y = -3x + 1$
$y = -\frac{3}{4}x + \frac{1}{4}$
Slope $m_1 = -\frac{3}{4}$

For $4x - 3y = 2$:
$-3y = -4x + 2$
$y = \frac{4}{3}x - \frac{2}{3}$
Slope $m_2 = \frac{4}{3}$

Step2: Check slope relationship

Multiply the slopes:
$m_1 \times m_2 = -\frac{3}{4} \times \frac{4}{3} = -1$
Lines are perpendicular if product = -1.

Answer:

C. perpendicular.