Match each of the following with the equations below. Write the letter of the appropriate equation in the column besides each

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.

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.

Dog

Step-by-step explanation:

Woof woof Woof Woof woof

Step-by-step explanation:

1) B

2) A

3) C

4) D