Question

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?

Drag each choice into the boxes to correctly complete the table

y= -1/2x+5
-2x+y=-4
-x+2y=2
x+2y=-2

Answer 1

y=-1/2x+5 is parallel.
-2x+y=-4 is perpendicular.
-x+2y=2 is neither.
x+2y=2 is parallel.
Hope this helps

Answer 2

We need to rewrite
`x+2y=6`, in slope intercept form.

`\Rightarrow 2y=-x+6`,

`\Rightarrow y=-(1)/(2)x+3`

The given equation has a slope of
`-(1)/(2)`.

ANSWER TO QUESTION 1

We now the write given options also in slope intercept form.

For the first one, we have

`y=-(1)/(2)x+5`

This first equation also has a slope of
`-(1)/(2)`.

Hence
`y=-(1)/(2)x+5` is parallel to
`x+2y=6`.

ANSWER TO QUESTION 2:

The second equation is;

`-2x+y=-4`.

We need to write this one too in slope intercept form.

`y=2x-4`

This second equation has a slope of 2

Since
`2* -(1)/(2)=-1`, the line
`-2x+y=-4`

is perpendicular to
`x+2y=6`.

ANSWER TO QUESTION 3

We rewrite the equation
`-x+2y=2` in slope intercept form.

`\Rightarrow 2y=x+2`

`\Rightarrow y=(1)/(2)x+1`

This equation also has a slope of
`(1)/(2)[\tex]</p><p>since the slope of [tex]-x+2y=2` is not equal to the slope of
`x+2y=6`, and the product of these two slopes
`(1)/(2) * - (1)/(2) \\e -1`, the two lines are neither parallel nor perpendicular.

QUESTION 4

The given line has equation
`x+2y=-2`. We rewrite this equation in the slope intercept form.

`\Rightarrow 2y=-x-2`

`\Rightarrow y=-(1)/(2)x-1`

This line has a slope of
`-(1)/(2)`.

Since this slope is the same as the slope of the given line,

`y=-(1)/(2)x-1` is parallel to
`x+2y=6`.

See graph in attachment.