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Parallel lines from equation

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

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  • aqualine ultimate style avatar for user Noah Fernandez
    I need help with finding the equation of a line parallel to another line. Say the first line has a slope of 2/5 and passes through (3, -5). How would I get the equation of a line parallel to that? My math book ain't helpin'.
    (17 votes)
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  • blobby green style avatar for user Nancy Christopher Becker
    How to prove lines parallel
    (3 votes)
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  • blobby green style avatar for user brooklyntevis
    does it matter if one of the slopes is negative and the other is positive? are they still parallel or not?
    (2 votes)
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  • blobby green style avatar for user nixmik
    what if you have y=3x+4 and it passes through (-2,3)
    (2 votes)
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    • female robot grace style avatar for user loumast17
      I'm assuming you want a line parallel to y = 3x + 4. All this means is that the slope will be 3 and the y intercept will not be 4. or in otherwords y = mx+b, m = 3 and b doesn't equal 4

      Now, as long as you have a slope and point you can find the equation of the line. And you do, you want a slope of 3 and a point (-2,3). To use this you use point slope form. y - y1 = m(x - x1) where (x1, y1) is the point you want. and m is slope. So just fill in and solve.

      y - y1 = m(x - x1) with m = 3 and (x1, y1) = (-2,3)
      y - 3 = 3(x - -2)

      If you prefer KC's way just start with y = 3x + b then b = y - 3x where you plug in (-2, 3) for x and y, or in other words:

      b = y - 3x where x = -2 and y = 3. Then again just plug in and solve. then plug b into y = 3x + b

      You get the same answer either way.
      (3 votes)
  • blobby green style avatar for user Jabes
    I don't understand every thing and i want to boost my grade
    (3 votes)
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  • starky sapling style avatar for user Banana
    What do you do if it tells you y=x? Like for example;
    y=x
    x+Y=-2?
    (2 votes)
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  • blobby green style avatar for user Tanisha
    I have a question, please answer it. Y = -4/3x + 6. Is this Perpendicular?
    (1 vote)
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  • starky sapling style avatar for user gyana kate
    at around Sal says you increase by one. I didn't see that in the equation anywhere, how did he get that?
    (1 vote)
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  • blobby green style avatar for user 251720
    i dont understand the concept at
    (1 vote)
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  • blobby green style avatar for user katishear
    Where can i find a video on how to do this problem
    Find the equation of a line in slope intercept form that is parallel to the line y = -2x - 3 that goes through the point (2, 1).
    I'm having a difficult time finding out how to do this
    (1 vote)
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Video transcript

We are asked which of these lines are parallel. So parallel lines are lines that have the same slope, and they're different lines, so they never, ever intersect. So we need to look for different lines that have the exact same slope. And lucky for us, all of these lines are in y equals mx plus b or slope-intercept form, so you can really just look at these lines and figure out their slope. The slope for line A, m is equal to 2. We see it right over there. For line B, our slope is equal to 3, so these two guys are not parallel. I'll graph it in a second and you'll see that. And then finally, for line C-- I'll do it in purple-- the slope is 2. So m is equal to 2. I don't know if that purple is too dark for you. So line C and line A have the same slope, but they're different lines, they have different y-intercepts, so they're going to be parallel. And to see that, let's actually graph all of these characters. So line A, our y-intercept is negative 6. So the point 0, 1, 2, 3, 4, 5, 6. And our slope is 2. So if we move 1 in the positive x direction, we go up 2 in the positive y direction. One in x, up 2 in y, if we go to in x, we're going to go up 4 in y. And I can just do up 2, then we're going to go 2, 4, and you're going to see it's all on the same line, so line A is going to look something like-- do my best to draw it as straight as possible. Line A-- I can do a better version than that-- line A is going to look like-- well, that's about just as good as what I just drew-- that is line A. Now let's do line B. Line B, the y-intercept is negative 6. 0, negative 6. So it has the same y-intercept, but its slope is 3, so if x goes up by 1, y will go up by 3. So x goes up by 1, y goes up by 3. If x goes up by 2, y is going to go up by 6. 2, 4, 6. So this line is going to look something like this. Trying my best to connect the dots. It has a steeper slope, and you see that when x increases, this blue line increases by more in the y direction. So that is line B-- and notice, they do intersect, there's definitely not two parallel lines. And then finally, let's look at line C. The y-intercept is 5. So 0, 1, 2, 3, 4, 5. The point 0, 5, its y-intercept. And its slope is 2. So you increase by 1 in the x direction, you're going to go up by 2 in the y direction. If you decrease by 1, you're going to go down 2 in the y direction. If you increase by, well, you're going to go to that point, you're going to have a bunch of these points. And then if I were to graph the line-- let me do it one more time-- if I were to decrease by two, I'm going to have to go down by 4, right? Negative 4 over negative 2 still a slope of 2, so 1, 2, 3, 4. And I can do that one more time, get right over there. And then you'll see the line. The line will look like that, it will look just like that. And notice that line C and line A never intersect. They have the exact same slope. Different y-intercepts, same slope, so they're increasing at the exact same rate, but they're never going to intersect each other. So line A and line C are parallel.