Question

0.04: swbat define, write, and graph equations of parallel and perpendicular lines. show all work and annotations for full credit. #1.) for the slopes listed below, write down the parallel slope and the perpendicular slope. slope: -1/2, 6, 3/4, -1/7, 9/2. parallel slope: blank, blank, blank, blank, blank. perpendicular slope: blank, blank, blank, blank, blank. #2.) line k || m and the equation of k is 4y - 5x = 20. line m passes through (8, -6). what is the equation of line m? a.) y = -4/5x - 40 b.) y = 5/4x - 16 c.) y = 1/5x + 16 d.) y = -5/4x + 4. #3.) two lines equations are 6x + 4y = 16 and y = 3/2x + 1. what statement is true? how do you know? a.) the lines are || b.) the lines are ⊥ c.) they are the same lines. explain: blank. #4.) determine a possible equation that is parallel to the line below. (there are many options!) equation: blank.

Explanation:

Step1: Recall slope - parallel and perpendicular rules

Parallel lines have equal slopes. If the slope of a line is $m$, the slope of a parallel line $m_{parallel}=m$. For perpendicular lines, if the slope of a line is $m$, the slope of a perpendicular line $m_{perpendicular}=-\frac{1}{m}$ (when $m
eq0$).

Step2: Find parallel and perpendicular slopes for #1

• For slope $m =-\frac{1}{2}$, $m_{parallel}=-\frac{1}{2}$, $m_{perpendicular}=2$.
• For slope $m = 6$, $m_{parallel}=6$, $m_{perpendicular}=-\frac{1}{6}$.
• For slope $m=\frac{3}{4}$, $m_{parallel}=\frac{3}{4}$, $m_{perpendicular}=-\frac{4}{3}$.
• For slope $m =-\frac{1}{7}$, $m_{parallel}=-\frac{1}{7}$, $m_{perpendicular}=7$.
• For slope $m=\frac{9}{2}$, $m_{parallel}=\frac{9}{2}$, $m_{perpendicular}=-\frac{2}{9}$.

Step3: Solve #2

First, rewrite the equation of line $k$: $4y-5x = 20$ can be rewritten as $y=\frac{5}{4}x + 5$, so the slope of line $k$ is $\frac{5}{4}$. Since $k\parallel m$, the slope of line $m$ is also $\frac{5}{4}$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(8,-6)$ and $m=\frac{5}{4}$, we have $y+6=\frac{5}{4}(x - 8)$. Expanding gives $y+6=\frac{5}{4}x-10$, so $y=\frac{5}{4}x-16$.

Step4: Solve #3

Rewrite $6x + 4y=16$ as $y=-\frac{3}{2}x + 4$. The other line is $y=\frac{2}{3}x+1$. Since $-\frac{3}{2}\times\frac{2}{3}=- 1$, the lines are perpendicular.

Step5: Solve #4

Find the slope of the given line from the graph. The line passes through points $(0,-2)$ and $(2,-1)$. The slope $m=\frac{-1+2}{2 - 0}=\frac{1}{2}$. A possible parallel line equation in slope - intercept form is $y=\frac{1}{2}x+1$ (any line with slope $\frac{1}{2}$ is correct).

Answer:

#1:

Slope	$-\frac{1}{2}$	$6$	$\frac{3}{4}$	$-\frac{1}{7}$	$\frac{9}{2}$
Perpendicular Slope	$2$	$-\frac{1}{6}$	$-\frac{4}{3}$	$7$	$-\frac{2}{9}$

#2: b. $y=\frac{5}{4}x - 16$
#3: b. The lines are $\perp$
#4: $y=\frac{1}{2}x + 1$ (any line with slope $\frac{1}{2}$ is acceptable)