Answer:
C
A
B
D
Step-by-step explanation:
We know that equation of line in slope intercept form is y = mx+c where m is slope and c is y-intercept
We know that lines [tex]y=m_1x+c\,,\,y=m_2x+b[/tex] are parallel if [tex]m_1=m_2[/tex] and perpendicular if [tex]m_1\,m_2=-1[/tex].
For equation, [tex]y=\frac{x}{3}+2[/tex], slope is m=[tex]\frac{1}{3}[/tex]
For equation of form [tex]9x-3y=18[/tex]:
[tex]9x-3y=18\\3y=9x-18\\y=3x-6[/tex]
slope is m = 3
For equation [tex]-4x+8y=9[/tex]:
[tex]8y=4x+9\\y=\frac{x}{2}+\frac{9}{8}[/tex]
slope is [tex]\frac{1}{2}[/tex]
For equation [tex]y=\frac{-x}{3}+1[/tex]:
slope is [tex]m=\frac{-1}{3}[/tex]
For equation [tex]x=3y+21[/tex]:
[tex]x=3y+21\\y=\frac{x}{3}-7[/tex]
Slope is [tex]m=\frac{1}{3}[/tex]
For equation x-2y=-2:
[tex]x-2y=-2\\y=\frac{x}{2}+1[/tex]
Clearly line x = 3 is perpendicular to y = 0
As slope of line [tex]y=\frac{x}{3}+2[/tex] is same as slope of [tex]x=3y+21[/tex], so they are parallel.
Slope of equation [tex]9x-3y=18[/tex] × slope of equation [tex]y=\frac{-x}{3}+1[/tex] = [tex]3\times \frac{-1}{3}=-1[/tex]
So, equations [tex]9x-3y=18\,,\,y=\frac{-x}{3}+1[/tex] are perpendicular.
Also, slope of equation [tex]-4x+8y=9[/tex] is same as slope of [tex]x-2y=-2[/tex], so equations [tex]-4x+8y=9\,,\,x-2y=-2[/tex] are parallel.
