Question

geo 10/9 10/10 slopes and equations of parallel and perpendicular lines
parallel and perpendicular lines were concepts you first learn in algebra 1. watch the videos, get notes and then start the problems. for 1 - 12 answer with \m = ___\ when you give the slope.
find the slope of a line parallel to each given line.

1. x = 5
2. y = -\frac{3}{2}x + 2
3. y = -2x + 3
4. y = -3x - 4
5. y = \frac{8}{3}x + 4
6. y = -\frac{9}{4}x - 4

find the slope of a line perpendicular to each given line.

1. x = -3
2. y = -2x + 3
3. y = 6x + 1
4. y = -x + 1
5. y = \frac{1}{5}x
6. y = -\frac{3}{4}x + 2

Explanation:

Step1: Recall slope - parallel line rule

Parallel lines have the same slope. For a line in the form $y = mx + b$, $m$ is the slope. A vertical line $x = a$ has an undefined slope.

Step2: Analyze line $x = 5$

The line $x = 5$ is vertical. A line parallel to it is also vertical and has an undefined slope.

Step3: Analyze line $y=-\frac{3}{2}x + 2$

The slope of the line $y=-\frac{3}{2}x + 2$ is $m =-\frac{3}{2}$. A line parallel to it has slope $m =-\frac{3}{2}$.

Step4: Analyze line $y=-2x + 3$

The slope of the line $y=-2x + 3$ is $m=-2$. A line parallel to it has slope $m=-2$.

Step5: Analyze line $y=-3x - 4$

The slope of the line $y=-3x - 4$ is $m=-3$. A line parallel to it has slope $m=-3$.

Step6: Analyze line $y=\frac{8}{3}x + 4$

The slope of the line $y=\frac{8}{3}x + 4$ is $m=\frac{8}{3}$. A line parallel to it has slope $m=\frac{8}{3}$.

Step7: Analyze line $y=-\frac{9}{4}x - 4$

The slope of the line $y=-\frac{9}{4}x - 4$ is $m=-\frac{9}{4}$. A line parallel to it has slope $m=-\frac{9}{4}$.

Step8: Recall slope - perpendicular line rule

If two non - vertical lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1m_2=-1$. A line perpendicular to a vertical line $x = a$ is a horizontal line with slope $m = 0$.

Step9: Analyze line $x=-3$

The line $x=-3$ is vertical. A line perpendicular to it is horizontal with slope $m = 0$.

Step10: Analyze line $y=-2x + 3$

If $m_1=-2$, then from $m_1m_2=-1$, we have $-2m_2=-1$, so $m_2=\frac{1}{2}$.

Step11: Analyze line $y = 6x+1$

If $m_1 = 6$, then from $m_1m_2=-1$, we have $6m_2=-1$, so $m_2=-\frac{1}{6}$.

Step12: Analyze line $y=-x + 1$

If $m_1=-1$, then from $m_1m_2=-1$, we have $(-1)m_2=-1$, so $m_2 = 1$.

Step13: Analyze line $y=\frac{1}{5}x$

If $m_1=\frac{1}{5}$, then from $m_1m_2=-1$, we have $\frac{1}{5}m_2=-1$, so $m_2=-5$.

Step14: Analyze line $y=-\frac{3}{4}x + 2$

If $m_1=-\frac{3}{4}$, then from $m_1m_2=-1$, we have $-\frac{3}{4}m_2=-1$, so $m_2=\frac{4}{3}$.

Answer:

1. Undefined
2. $m =-\frac{3}{2}$
3. $m=-2$
4. $m=-3$
5. $m=\frac{8}{3}$
6. $m=-\frac{9}{4}$
7. $m = 0$
8. $m=\frac{1}{2}$
9. $m=-\frac{1}{6}$
10. $m = 1$
11. $m=-5$
12. $m=\frac{4}{3}$