# Math Is Fun Forum

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## #1 2021-07-20 02:15:13

Hannibal lecter
Member Registered: 2016-02-11
Posts: 282

### Find equations for the lines through the point

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

can lines be parallel to and perpendicular to at same time? I just didn't understand what is the meaning of ( parallel to and perpendicular to )

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

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## #2 2021-07-20 19:38:58

Bob Registered: 2010-06-20
Posts: 9,271

### Re: Find equations for the lines through the point

hi

The English language can produce some ambiguous sentences at times.  The question asks for equations.  What the questioner means is find one equation where a line is parallel and another where a line is perpendicular.

I would start with y + 4x = 7 and re-arrange it so that y is the subject ie. y = ......

So that would be y = -4x + 7

So the gradient for a parallel line has m = -4

So start with y = -4x + c.  Substitute x = 1 and y = 5 to calculate c.

To get the perpendicular line make use of the fact that if gradients m and n are perpendicular then mn = -1

This rule is explained in post #3 in this thread: http://www.mathisfunforum.com/viewtopic.php?id=26175

So the second equation has the form y = (1/4) . x + c  Once again you can use (1,5) to find c.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline

## #3 2021-07-23 04:44:12

Mark Dater
Member
Registered: 2021-07-23
Posts: 12

### Re: Find equations for the lines through the point

So you have to take 1.5?

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