Question

2.11 practice

1. find the slope of a line perpendicular to the line whose equation is $3x + 2y = -2$. fully simplify your answer.

Explanation:

Step1: Rewrite in slope-intercept form

Rearrange $3x + 2y = -2$ to $y = mx + b$:
$$2y = -3x - 2$$
$$y = -\frac{3}{2}x - 1$$

Step2: Identify original slope

The slope of the given line is $m_1 = -\frac{3}{2}$.

Step3: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$$m_2 = \frac{2}{3}$$

Answer:

$\frac{2}{3}$