Question

which equation represents a line which is perpendicular to the line $8x + 3y = 3$?
answer
$\circ$ $y = \frac{3}{8}x - 4$ $\circ$ $y = -\frac{3}{8}x - 7$
$\circ$ $y = -\frac{8}{3}x + 5$ $\circ$ $y = \frac{8}{3}x - 5$

Explanation:

Step1: Rewrite given line to slope-intercept form

Start with $8x + 3y = 3$. Isolate $y$:
$$3y = -8x + 3$$
$$y = -\frac{8}{3}x + 1$$

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals. For slope $m_1 = -\frac{8}{3}$, the perpendicular slope $m_2$ is:
$$m_2 = \frac{3}{8}$$

Step3: Match slope to options

Identify the option with slope $\frac{3}{8}$.

Answer:

$y = \frac{3}{8}x - 4$