Question

Line a is represented by the equation y=−2x+3 .

How do these equations compare to line a?


Parallel to line a
Perpendicular to line a
Neither parallel nor perpendicular to line a

y=2x-1
y=-2x+5
y=1/2x+7

Answer 1

the second line of eauation y=-2x+5 is parallel to a since both have the same slope which is -
-2
the first line of equation y=2x-1 is neither perpendicular nor parallel to a since the (slope of this line) x (the slope of a) = 2 x -2 = -4 not -1, so they aren't perpendicular and its slope isn't equal to that of a, so they aren't parallel
the last line of equation y=1/2x+7 is perpendicular to a since (the slope of a) x (the slope of this line) = -2 x 1/2 = -1

Answer 2

A.Neither perpendicular nor parallel to line a

B.Parallel to line a

C.Perpendicular to line a

Explanation:

We are given that line a represented by the equation

`y=-2x+3`

Slope- intercept form of line is given by

`y=mx+C`

Where m=Slope of line a

C=y- intercept

Comparing it with the given equation then, we get

Slope of line a=-2

We know that

When two lines are parallel then their slopes are equal.

When two lines are perpendicular then

Slope of one line=
`-(1)/(slope\;of\;other\;line)`

A.
`y=2x-1`

Compare it with
`y=mx+C`

We get slope of line,m=2

Slope of the line is opposite to slope of line a .

Hence, it is neither perpendicular nor parallel to line a .

B.
`y=-2x+5`

Compare it with
`y=mx+C`

m=-2

It is parallel to line a because slope of both lines are equal.

C.
`y=(1)/(2)x+7`

Compare it with
`y=mx+C`

We get slope of line , m=
`(1)/(2)`

Slope of the line=
`-(1)/(slope\;of\;line\;a)=(1)/(2)`

Hence, the line is perpendicular to the line a.