If you are given two linear equations, how will you say that two lines they represent are parallel or perpendicular to each other.

A general linear equation is y=mx + c. To determine whether 2 lines are parallel or perpendicular you need to look at the gradient of the equation ( the m bit ).
e.g. y=2x+5, the gradient is 2. if 2 lines are parallel, then their gradients will be identical. If 2 lines are to be perpendicular to each other, then the product( i.e.. What you get when you multiply them together) will be equal to -1.

e.g.. Find a line perpendicular to the line y=2x+5.
The gradient = 2. If m equals gradient of the line we need to find out, then 2*m = -1
m = -1/2. So the line will have equation y= -x/2 + c ( where c can be any number)

Put the two equations in the following forms:

y = mx + c

y = nx + d


if m = n then parallel

If mn = -1, perpendicular

how would you solve
-10-2x=5y
-5x+2y=-2
to find out whether its parallel, perpendicular, or neither

Quote:

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Originally Posted by temiquel

how would you solve
-10-2x=5y
-5x+2y=-2
to find out whether its parallel, perpendicular, or neither

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As noted in the earlier posts, put the two equations into the form y = mx+b and compare the values of the m's.