Question

consider the line $y = -5 - \frac{3}{4}x$. 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: Identify the slope of the given line

The given line is in the form \( y = mx + b \), where \( m \) is the slope. For the line \( y=-5-\frac{3}{4}x \) (which can be rewritten as \( y = -\frac{3}{4}x - 5 \)), the slope \( m \) of the given line is \( -\frac{3}{4} \).

Step2: Find the slope of a parallel line

Parallel lines have equal slopes. So, the slope of a line parallel to the given line will be the same as the slope of the given line, which is \( -\frac{3}{4} \).

Step3: Find the slope of a perpendicular line

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal of \( m \). The negative reciprocal of \( -\frac{3}{4} \) is calculated as follows: First, take the reciprocal of \( -\frac{3}{4} \), which is \( -\frac{4}{3} \), then take the negative of that, so \( \frac{4}{3} \).

Answer:

Slope of a perpendicular line: \(\frac{4}{3}\)
Slope of a parallel line: \(-\frac{3}{4}\)