Question

hw 7: introduction to geometry
score: 9/16 answered: 10/16
question 11
consider the equation 6x - 4y = - 8
a line parallel to the above line would have a slope of
a line perpendicular to the above line would have a slope of
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Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Starting with $6x−4y=-8$, we solve for $y$. First, subtract $6x$ from both sides: $-4y=-6x - 8$. Then divide by $-4$: $y=\frac{6}{4}x + 2=\frac{3}{2}x+2$. The slope of the given line is $m=\frac{3}{2}$.

Step2: Find slope of parallel line

Parallel lines have the same slope. So the slope of a line parallel to the given line is $\frac{3}{2}$.

Step3: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope $m$ is $-\frac{1}{m}$. Since $m = \frac{3}{2}$, the slope of the perpendicular line is $-\frac{2}{3}$.

Answer:

Slope of parallel line: $\frac{3}{2}$
Slope of perpendicular line: $-\frac{2}{3}$