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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
i think it is a

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Other answers:

a is the first set of choices?
u should write the options properly to make them more understandable particularly the perpendicular lines
ok
hold on
a:\[y=2x-7\]
|dw:1433696367134:dw|
|dw:1433696418674:dw|
@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?
parallel lines have asme slope different y-intercepts
Correct.
to ahnge to perpinduculat make the slope negative and the reciprocal?
Correct.
reciprocal is like 4/1 changef to 1/4
Yes.
i am sure you know that was just in case you were going to sake me :D
*ask
is a correct? i know that c and d are not correct
because of them for parallel they do not have the asme slope
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.
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?
1=6+b -6 -6?
2 * 4 = 8, not 6.
-8 srry than b=-7?
Then subtract 8 from both sides.
Yes. Since we now have b = -7, the parallel line is: \(y = 2x - 7\)
Now we can work out the perpendicular line in a similar way.
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?
-1/2?
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.
\(y = -\dfrac{1}{2}x + b\) \(1 = \left( -\dfrac{1}{2} \right) (4) + b\) What is b?
3
Great. The equation of the perpendicular line is: \(y = -\dfrac{1}{2} x + 3\)
Now choose the correct choice from the answers.
is still say a @mathstudent55
Yes, A is the answer.
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