Question

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

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

Answer:

A.Neither perpendicular nor parallel to line a

B.Parallel to line a

C.Perpendicular to line a

Step-by-step 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=$-\frac{1}{slope\;of\;other\;line}$

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.$y=\frac{1}{2}x+7$

Compare it with $y=mx+C$

We get slope of line , m=$\frac{1}{2}$

Slope of the line=$-\frac{1}{slope\;of\;line\;a}=\frac{1}{2}$

Hence, the line is perpendicular to the line a.