Line l is defined by the equation y – 5x = 4 and line w is d

Hi Bunuel,
If we are given two lines (and know their slopes), can we calculate the degree that their intersection makes?
What's the formula for that?

Bunuel,
Sorry for my ignorance but is it a fact that two lines in any plane, if they don't intersect, they MUST be parallel?

On the GMAT, all figures lie in a plane unless otherwise indicated. So, lines l, w and k are in the same plane. Next, if two lines that are in the same plane do not intersect, the two lines are parallel. Thus, line k does not intersect line l, means that lines k and l are parallel.

Hope it's clear.

Bunuel: Hope it's Clear

Me: Crystal.

Thank you.

It is important to understand and have a visual map of this question- what this questions basically means when it states that all lines lie in one plane simply means- well within the context of the GMAT as Bunuel already stated- that all lines exist on a two dimensional plane. So if you draw out a chart/ plane with 4 quadrants as usual on a piece of paper then there's no way to have two lines that do not intersect and are not parallel. In simpler terms, if two lines do not intersect then they MUST be parallel. Also, do not confuse line k with l or w- basically this question gives you two equations for two lines because these lines are perpendicular.

Line L
10y= -2x -20=
y = -2/10x - 20
y= -1/5x - 2

Line W
y= 4 +5x
y= 5x + 4 ( commutative property of addition)

Because line K does not intersect L it MUST be parallel to L and if line K is parallel to L then it is also perpendicular to W- and perpendicular simply means it forms a 90 degree angle. Perpendicular lines are also important for circle questions on the GMAT. Some of the concepts should hopefully carry over- so some of the common traps and shortcuts in coordinate geometry problems on the GMAT will help with PS and DS questions in regular geometry and vice versa.

Yes. Use the formula

TanX = m1-m2/(1+m1m2)

where X is the angle between the lines and m1 and m2 are the slopes.

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I have one doubt regarding this question. I get it that you chose 90 degrees because of the slopes. But it also says that these lines don't intersect which means they are parallel. So the angle should be 0 degrees isn't it?

Posted from my mobile device

An excellent question that tests multiple co-ordinate geometry concepts without requiring tons of calculation.

Slope of line l is 5 (y = 5x + 4)

Since line k does not intersect line l, line k & l are parallel.

So, slope of line k is also 5.

Slope of line w is -1/5 (Derived from 10y + 2x + 20 = 0)

So, line k & w are perpendiculars to each other. In other words, the angle formed by line k and line w is 90 degree.

Option: D

"Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other (Bunuel)."

Can someone explain or show why this is? Do you have to memorize this fact to get the question right, or is there another way?

Thank you!!

Yes, GMAT expects you to know this.

You can draw a line with a slope of 5 and another line with a slope of -1/5. The lines will be perpendiculars to each other.

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