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solmaris [256]
2 years ago
9

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

Mathematics
2 answers:
BartSMP [9]2 years ago
5 0
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
Free_Kalibri [48]2 years ago
3 0

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.

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