Question

consider the line -5x - 3y = 9. what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line? slope of a perpendicular line: slope of a parallel line:

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $-5x - 3y = 9$ to $y = mx + b$:
$$-3y = 5x + 9$$
$$y = -\frac{5}{3}x - 3$$

Step2: Identify original slope

The slope $m$ of the given line is $-\frac{5}{3}$.

Step3: Find parallel slope

Parallel lines have equal slopes:
$$m_{\text{parallel}} = -\frac{5}{3}$$

Step4: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$$m_{\text{perpendicular}} = \frac{3}{5}$$

Answer:

Slope of a perpendicular line: $\frac{3}{5}$
Slope of a parallel line: $-\frac{5}{3}$