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**Hannibal lecter****Member**- Registered: 2016-02-11
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Hi,

can two lines be perpendicular and parallel at the same time?

if not...then what is mean the following ? :-

Find equations for the lines through the point (1,5) that are parallel to and perpendicular to the lines the equation y + 4x =7

if the answer is not how can that be " that are parallel to and perpendicular to .. " ???

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No, you need to find two lines: one which is parallel to y = 4x + 7, and one which is perpendicular to it, each of which pass through (1,5).

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**Hannibal lecter****Member**- Registered: 2016-02-11
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how can that be in a graph drawing

I know the slop is 1/4

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Let's start with finding the parallel line through (1,5).

Can you write down a line which is parallel to y = 4x + 7?

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**Hannibal lecter****Member**- Registered: 2016-02-11
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it's

y= 1 +4x right?

Wisdom is a tree which grows in the heart and fruits on the tongue

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Correct! And you can check your answer by substituting x = 1 into your answer to get y = 5.

Now for the perpendicular line passing through (1,5). The line y = 4x + 7 has a gradient of 4. What is the gradient of the perpendicular line?

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I know it's -1/4

what after that?

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Yes, so if the perpendicular line has a gradient of , then the line must be of the form . Given that the line passes through , can you find the value of ?

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I think It's -1/-4 which gives 1/4 positive not negative I think my answer was not correct

so the line is y=0.25x + 4.75

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No, it's -1/4: the gradient of a line and the gradient of the line perpendicular to it must multiply to make -1.

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**Hannibal lecter****Member**- Registered: 2016-02-11
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sorry but the orignal line was y = -4x + 7 the slop not positive I'm talking about this case

but thanks anyway I solved all the question about that field

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Ah, I see -- my apologies, I misread the original equation. In that case, you are completely correct.

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