Math / Geometry

QuestionConsider the line $y=\frac{2}{3} x-2$ What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Slope of a parallel line: $\square$
Slope of a perpendicular line: $\square$

Studdy Solution

STEP 1

1. The given line equation is in the slope-intercept form $y = mx + b$ , where $m$ represents the slope.
2. Parallel lines have the same slope.
3. Perpendicular lines have slopes that are negative reciprocals of each other.

STEP 2

1. Identify the slope of the given line.
2. Determine the slope of a line parallel to the given line.
3. Determine the slope of a line perpendicular to the given line.

STEP 3

Identify the slope of the given line $y = \frac{2}{3}x - 2$ . The slope of the line is the coefficient of $x$ , which is $\frac{2}{3}$ .

STEP 4

Determine the slope of a line parallel to the given line. Parallel lines have the same slope. Thus, the slope of a line parallel to $y = \frac{2}{3}x - 2$ is $\frac{2}{3}$ .

STEP 5

Determine the slope of a line perpendicular to the given line. Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of $\frac{2}{3}$ is $-\frac{3}{2}$ . Thus, the slope of a line perpendicular to $y = \frac{2}{3}x - 2$ is $-\frac{3}{2}$ .
Solution: Slope of a parallel line: $\frac{2}{3}$
Slope of a perpendicular line: $-\frac{3}{2}$

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