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## High school geometry

### Unit 6: Lesson 5

Equations of parallel & perpendicular lines- Parallel lines from equation
- Parallel lines from equation (example 2)
- Parallel lines from equation (example 3)
- Perpendicular lines from equation
- Parallel & perpendicular lines from equation
- Writing equations of perpendicular lines
- Writing equations of perpendicular lines (example 2)
- Write equations of parallel & perpendicular lines
- Proof: parallel lines have the same slope
- Proof: perpendicular lines have opposite reciprocal slopes
- Analytic geometry FAQ

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# Parallel lines from equation (example 2)

CCSS.Math:

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

## Want to join the conversation?

- Two lines that are the same are not parallel, right?(9 votes)
- Alex,

You are correct. If two lines are the same line, then there is only one line, not two parallel lines.(32 votes)

- What is the difference between a parallel line and a perpendicular line?(5 votes)
- Parallel lines: \\ or || or // (they will never intersect with each other)

Perpendicular lines: 丄 (they intersect with each other, forming a right angle)(7 votes)

- How do I find the distance between two parallel lines?(7 votes)
- Choose a point on one of the lines (x1,y1).

The distance between the lines is then the perpendicular distance between the point and the other line. If you rewrite the equation of the line in standard form Ax+By=C, the distance can be calculated as:

|A*x1+B*y1-C|/sqroot(A^2+B^2).

It can also be calculated with slope-intercept form as:

|y1-(m*x1+b)|/sqrt(1+m^2)(8 votes)

- Isn't B perpendicular to A or C?(6 votes)
- Chuck is right

Just a quick correction (to avoid possible confusion):

The slope for A and C is 3/4 , and the slope for B is -3/4(6 votes)

- what does y intercept i.e b mean?(4 votes)
- A y-intercept is where a function intersects the y axis. That happens when x=0.(6 votes)

- The constants don't seem necessary in determining slope. Could we leave them out and calculate y = mx + (not needed) when determining parallel lines? What about for perpendicular lines?(4 votes)
- The constants are not necessary to determine the slope. Two lines are parallel when their slopes are the same, so constants are not needed then, unless you need to figure out if two different-seeming lines are in fact the same line, which some people may need in some circumstances. The Constants are important though if you plan to map either of the lines on a graph, so don't discard them entirely! :)(6 votes)

- 'Neither one of the other two'? isn't that a double negative?(2 votes)
- Yes, indeed it is. The subtitles say "either" instead of "neither" if anyone gets confused about the wording. Good thing this is a video on math, and not about grammar!(3 votes)

- howdy when they say find a ordered pair on a parallel line for example x= -2 what do they mean(1 vote)
- this means that you take any line parallel to the line x=-2, and pick any point (x,y) on that line. :-) hope this helps!(3 votes)

- Wait... why does the "y" change to an "m" and then to a "b"? Can someone please explain? Is there some kind of pattern?(1 vote)
- y does not change to anything, the slope intercept form of a linear equation is y=mx+b where m is the slope and b is the intercept. Sal is breaking the equations apart to get values of m and b, not changing anything.(3 votes)

- I'm a little bit confused and want clarification.

If I have to answer a question, for example:

"Are the slopes given perpendicular,parallel, or neither?"

And the slopes given is m= 3/4 and m=-3/4,

My answer would have to be 'perpendicular', am I wrong?(0 votes)- Yes, you're wrong. Perpendicular lines have negative reciprocal slopes, not merely negative slopes. Lines with slopes of 3/4 and -3/4 are neither parallel nor perpendicular.(4 votes)

## Video transcript

We have three lines and we have
to figure out which of the three are parallel. So line A-- and it can't be
parallel on its own, it has to be parallel to another
of the three lines. So the equation for line
A is y is equal to 3/4 x minus four. Line B is 4y minus 20 is
equal to negative 3x. And then line C is negative
3x plus 4y is equal to 40. So to figure out if any of these
lines are parallel to any of the other lines,
we just have to compare their slopes. If any two of these lines have
the same slope and they're different lines, they have
different y-intercepts, then they're going to be parallel. Now line A, it's very easy
to figure out its slope. It's already in slope-intercept
form. This is mx plus b, the slope
is 3/4 and the y-intercept, which isn't as relevant when
you're figuring out parallel lines, is negative 4. So let's see what the other
character's slopes are. This isn't in any kind
of standard form. It's not a standard form,
slope-intercept, or point-slope form, but let's
see what the slope of this line is. So to get it into
slope-intercept form, which is really the easiest one to pick
out the slope from, let's add 20 to both sides of
this equation. The left-hand side, those cancel
out, that was the whole point, you get 4y is equal
to negative 3x plus 20. And now we can divide
everything by 4. We are left with y is equal
to negative 3/4 x plus 5. So in this case, y-intercept
is 5, but most importantly, the slope is negative 3/4, so
it's different than this guy. This is negative 3/4, this is
positive 3/4, so these two guys definitely aren't
parallel. Let's move on of this guy
in standard form. So let's get the x term
on the other side. So let's add 3x to both sides
of this equation. Left-hand side, these
cancel out. We're just left with 4y is equal
to 3x plus 40, or 40 plus 3x, either way. Now we can divide both sides
by 4 you have to divide every term by 4. The left-hand side, you're
left with y. The right-hand side, you
have 3/4 x plus 10. So here, our slope is 3/4 and
our y-intercept, if we care about it, is 10. So this line and this line have
the exact same slope, 3/4, and they're different
lines because their y-intercept is different. So we know that A and C are
parallel lines and B is not parallel to either one
of the other two.