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Parallel lines from equation (example 3)

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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  • leaf grey style avatar for user xcrypt
    When two lines have the same slope, but they also have the same y-intercept (they lie on each other), are they considered parallel?
    (48 votes)
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  • blobby green style avatar for user Ricky Brown
    (5, -5), parallel to y = - 3\5 x + 2
    (7 votes)
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    • duskpin sapling style avatar for user Vu
      Using y=mx+b
      if it is parallel, means it has the same slope.
      So your slope m = -3/5
      the coordinate (x,y) is (5,-5)
      So your x=5 and y=-5
      Now you can substitute them into y=mx+b and solve for b.
      (6 votes)
  • leaf green style avatar for user Gemma Hyeon
    At for the slope formula of y=6 i thought the slope is 6 and the y intercept is 0? Is that right? If not, why isn't it?
    (4 votes)
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  • ohnoes default style avatar for user keckkhamari8
    at why do you divde them all by 2??
    (2 votes)
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    • primosaur ultimate style avatar for user Ignacy Sawa
      Line A equation is given as 2y = 12x + 10
      We use slope of the line to find out if lines are parallel. Slope is read easily from the slope-intercept form, which looks like this:
      y = ax + b (where a is the slope)
      So how can we easily turn 2y = 12x + 10 into something that starts with "y = "?

      .
      .
      .

      We divide both sides of the equation by 2 :)
      (7 votes)
  • starky sapling style avatar for user Banana
    Are lines that are negative reciprocals perpendicular?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      Yes, but you will probably often see different wording. The way you might hear it is that perpendicular lines have opposite reciprocal slopes. You should have the word slope somewhere in your question. The idea is that if it is positive, the perpendicular line would have a negative slope, but if the line has a negative slope, then the perpendicular would have a positive slope. If the slope of a line is -3, then the perpendicular line has a slope of 1/3.
      (6 votes)
  • marcimus pink style avatar for user t2sporty
    hello. i don't know how to solve this problem. i have to find the equation:
    intersects with y=2x-1 on the y-axis and is parallel to y=-x
    Thank you!
    (3 votes)
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  • male robot johnny style avatar for user MarianSedrak1
    If I have 2 slopes for example 150\120 and my second slope 125/100 are they opposite reciprocal slope?
    (4 votes)
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  • starky seed style avatar for user Dj Khaled Junior
    What if for Line B x=6 what would we need to do then?
    (4 votes)
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  • blobby green style avatar for user Brian Wegemann
    How would I write an equation with parallel lines? An example is: write an equation through (9,-1) and parallel yo y=-5x+7.
    (2 votes)
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    • blobby green style avatar for user Martin
      Your given line y = -5x +7, is in slope intercept form, so you can see the slope is -5.
      Use the point slope form to quickly write an equation. Because the line you want is parallel, you know it has the same slope as your given line.
      So the parallel line will also have slope -5. It goes thru (9.-1);
      Point slope form is y - y1 = m (x - x1); here y1 = -1 and x1= 9 and m=-5
      y - -1 = -5(x -9)
      y+1 = -5(x-9)
      With a little algebra you can change this to slope intercept form if you need that.
      (3 votes)
  • blobby green style avatar for user hera8859
    When two lines have the same slope, but they also have the same y-intercept (they lie on each other), are they considered parallel? And how
    (2 votes)
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Video transcript

We're asked which of these lines are parallel. So they give us three equations of three different lines and if they're parallel, then they have to have the same slope. So all we have to do over here is figure out the slopes of each of these lines, and if any of them are equal, they're parallel. So let's do line A. Line A, it's 2y is equal to 12x plus 10. We're almost in slope-intercept form, we can just divide both sides of this equation by 2. We get y is equal to 6x-- right, 12 divided by 2 -- 6x plus 5. So our slope in this case, we have it in slope-intercept form, our slope in this case is equal to 6. Let's try line B. Line B is y is equal to six. You might say this hey, this is a bizarre character, how do I get this into slope-intercept form, where's the x? And my answer to you is that it already is in slope-intercept form. I could just rewrite it as y is equal to 0x plus 6. The x term is being multiplied by 0 because the slope here is 0. y is going to be equal to six no matter how much you change x. Change in y is always going to be 0, it's always going to be 6. So here, our slope is 0, so these two lines are definitely not parallel, they have different slopes. So let's try line C. Line C-- I'll do it down here. Line C, so it's y minus 2 is equal to 6 times x plus 2. And this is actually in point-slope form, where the point x is equal to negative 2, y is equal to 2. So the point negative 2, 2, is being represented here because you're subtracting the points. And the slope is 6, so we already know that the slope is equal to 6. And sometimes people are more comfortable with slope-intercept form, so let's put it in slope-intercept form just to confirm that if we put it in this form, the slope will still be equal to 6. So if we distribute the 6, we get y minus 2 is equal to 6 times x, 6x, plus 6 times 2 is 12. And if you add this 2 -- if you add 2 to both sides of the equation, you get y-- because these guys cancel out-- is equal to 6x plus 14. So you see, once again, the slope is 6. So line A and line C have the same the slope, so line A and line C are parallel. And they're different lines. If they had the same y-intercept, then they would just be the same line.