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# Perpendicular lines from equation

Sal determines which pairs out of a few given linear equations are perpendicular. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What is an equivalant line? It says in the example I have a choise between perpendicular lines, paralel lines, equivalant lines, and so forth. Thank You!
• Equivalent lines are what they say, the same lines! Let's say you're given this example: 5x+y=2 and 20x+4y=8 and you have to figure out what kind of line this is. This would be an equivalent line because you can make the 2 equations the same by multiplying 5x+y=2 by 4 to get the other equation 20x+4y=8 so they are equivalent lines. I really stink at explaining stuff, unlike Sal but I tried my best and I hope this helped! :)
• Could you prove that slopes of perpendicular lines are negative inverses of each other using trigonometry?
• Yes, you can use triangles to prove the slopes are inverses.
Imagine a line from 0,0 to 3,4. At 3,4 you can draw a right triangle with the axis and the point 0,0.
Now imagine a perpendicular line, that intersect at the point 3,4. You can make another triangle from 3,4 to the axis.
The 2 triangles are complementary because the 2 acute angles at the intersection sum 90 degrees, and the 2 triangles have a right angle.
So the relationship between the sides of the 2 triangles is the inverse. And, if the relationship between the sides is the inverse, the slopes of the triangles are inverse also.
But also negative!!! Why? I don't use trigonometry but it's pretty simple.
If a line goes up, positive slope, the perpendicular goes down, negative slope. If a line goes down, negative slope, the perpendicular goes up, positive slope.
• At Sal tells me that perpendicular lines must intersect with a right angle.
Parallel lines never meet because they have the same slope...
So what exactly is it when to lines cross, but not with 90 degree angle?
• They just intersect. Nothing fancy
• Is there a more rigid definition for perpendicularity? A line of the form y = C has a slope of 0. There is no negative reciprocal for 0, but a line of the form x = C is still perpendicular.
• Thanks for the feedback. The problem with your definition is that it does not cover the case for a horizontal and vertical line which are perpendicular, but the product of their slopes are 0, not -1. I think the wikipedia definition I found covers this limit case.
• In a square can there be perpendicular line segments?
• All the sides of a square are perpendicular. If you considered the sides as line segments, then yes, there can be perpendicular line segments.
(1 vote)
• No, they can have different y-intercepts. To be perpendicular, they only need to have opposite reciprocal slope. For example, the lines, y=3x+8 and y= -(1/3)x-3 would be perpendicular because -1/3 is the opposite reciprocal of 3.
• we have 2 lines y = 3x and y = -3x, where slops are 3 and -3, they intersect at origin with 90 degree. but as explained in video it should not be true right
• The issue is that they do not intersect at 90-degree angles. You would need 3 and -1/3 or 1/3 and -3 to have intersections at 90 degrees.
• If you have two equations of lines, how do you tell if they even intersect, not just if they're perpendicular?
• You look at the slope (which either is clearly visible in the equation or you can compute it easily from the coefficients of x and y in the equation). If slopes are the same then the lines are either equivalent (both equations describe the same line) or parallel (and thus do not intersect).

Two lines with different slopes will always intersect.
• How do I know such the equation is or not a Perpendicular line from the equation? What number the slope need be? It isn't the inverse, right?
• For perpendicular lines, the slopes must be opposite reciprocals (different signs and fraction inverted). So -3 and 1/3 or 2/3 and -3/2 are pairs of perpendicular slopes.
• can you give me an example about the perpendicular equation from the graph
• Issam,
A perpendicular line has a slope of the negative inverse of the original equations slope.

If y=2x+1 is the first equation, it has a slope of 2.
The negative inverse of 2 is -½ so a perpendicular line would be
y= -½x + ? And value can be used for the ? and the line remains perpendicular.

y= -½x + 3 would be perpendicular to y=2x+1
Here is what the linear equations look like on a graph: