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

]]>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 )

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