are the lines perpendicular? y= -x -4 ans 5x + 5y -20

Question

are the lines perpendicular?  y= -x -4 ans 5x + 5y -20

anonymous · Answer

is "ans" supposed to be "and"?

anonymous · Answer

lines are perpindicular if they have a negative inverse slope.

So a line with slope 3 is perpendicular to a line with slope -(1/3).

A line with slope -2 is perpendicular to a line with slope (1/2)

etc.

y = -x - 4 is the first equation, and its slope is the coefficient of the x-term, -1.

So the negative inverse of -1 would be -(-1)/1 = 1

Can you check the second line and find out if it has slope of 1?

anonymous · Answer

Nope. If you simplify the second equation you end up with the exact same as the first equation: y=-x-4. In order for two lines to be perpendicular, their slopes have to multiply to reach a product of -1. Here, both slopes are -1, so (-1)x(-1)=1. So no, the lines aren't perpendicular. They're the exact same line.

anonymous · Answer

That's a good explanation.

Lines can...
(1) intersect in exactly 1 point, 
(2) intersect in exactly one point AND be perpendicular if their slopes multiply to = -1, 
(3) not intersect at all if they are parallel, meaning they have the same slope, 
or (4), completely overlap each other, as just another name for the same line... y = x + 1  is the same exact line as 2y = 2x + 2