@mathstudent55

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@mathstudent55

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Select the equations that are parallel and perpendicular to y = 2x - 1 and that pass through the point (4, 1).
parallel: y = 2x - 7
perpendicular: y = negative one over twox + 3
parallel: y = 2x + 2
perpendicular: y = negative one over twox + four and one half
parallel: y = negative one over twox - 7
perpendicular: y = 2x + 3
parallel: y = -2x - 7
perpendicular: y = negative one over twox - 1

- help_people

i think it is a

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@mathstudent55

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## More answers

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@mathmate @mathmath333

- anonymous

a is the first set of choices?

- mathmath333

u should write the options properly to make them more understandable particularly the perpendicular lines

- help_people

ok

- help_people

hold on

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a:\[y=2x-7\]

- help_people

|dw:1433696367134:dw|

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|dw:1433696418674:dw|

- mathstudent55

@help_people
Do you know the relationship of the slopes of two parallel lines?
Do you know the relationship of the slopes of two perpendicular lines?

- help_people

parallel lines have asme slope different y-intercepts

- mathstudent55

Correct.

- help_people

to ahnge to perpinduculat make the slope negative and the reciprocal?

- mathstudent55

Correct.

- help_people

reciprocal is like 4/1 changef to 1/4

- mathstudent55

Yes.

- help_people

i am sure you know that was just in case you were going to sake me :D

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*ask

- help_people

is a correct? i know that c and d are not correct

- help_people

because of them for parallel they do not have the asme slope

- mathstudent55

Let's work on the parallel line first.
Given line:
\(y = 2x - 1\)
General equation of line in slope-intercept form:
\(y = mx + b\)
A parallel line has the same slope as the given line. We need a line with slope 2.

- mathstudent55

The parallel line has to have an equation of the form
\(y = 2x + b\) since we know its slope must be 2 just like the given line.
We are given point (4, 1), so let's plug in (4, 1), and find b.
\(1 = 2(4) + b\)
What do you get for b?

- help_people

1=6+b
-6 -6?

- mathstudent55

2 * 4 = 8, not 6.

- help_people

-8 srry than b=-7?

- mathstudent55

Then subtract 8 from both sides.

- mathstudent55

Yes.
Since we now have b = -7, the parallel line is:
\(y = 2x - 7\)

- mathstudent55

Now we can work out the perpendicular line in a similar way.

- mathstudent55

Now for the perpendicular line.
Given line:
\(y=2x−1\)
General equation of line in slope-intercept form:
\(y=mx+b\)
Perpendicular lines have slopes that are negative reciprocals of each other.
The given line has slope 2.
What is the negative reciprocal of 2?

- help_people

-1/2?

- mathstudent55

Correct.
We now insert the new slope in the slope-intercept form.
\(y = -\dfrac{1}{2}x + b\)
Now we insert the know point on the line and solve for b.

- mathstudent55

\(y = -\dfrac{1}{2}x + b\)
\(1 = \left( -\dfrac{1}{2} \right) (4) + b\)
What is b?

- help_people

3

- mathstudent55

Great.
The equation of the perpendicular line is:
\(y = -\dfrac{1}{2} x + 3\)

- mathstudent55

Now choose the correct choice from the answers.

- help_people

is still say a @mathstudent55

- mathstudent55

Yes, A is the answer.

- help_people

ty

- mathstudent55

yw

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