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Worked example: intercepts from an equation

Sal finds the x and y-intercepts of the equation 2y + 1/3x = 12. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • hopper jumping style avatar for user :)
    I know in the equation y=mx+b, b is the y-intercept. Is there a x-intercept in another slope equation? Thanks!
    (5 votes)
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    • aqualine ultimate style avatar for user Justin Barth
      Slope intercept form is y=mx+b. Really, it is more like "Rise/Run Slope of a line from the y-intercept form". If you want to know the x-intercept form you can solve the equation for x.

      y=2x+4 would become x=1/2y-2. Now plug in zero for y and you will have what x is equal to (-2). The reason we use y=mx+b is because the idea of rise/run no longer works correctly in this version of slope x-intercept. You have run/rise instead of rise/run. This is unwanted confusion as now you have

      y=mx+b "Rise/Run Slope of a line from the y-intercept form"
      and
      x=my+b "Run/Rise Slope of a line from the x-intercept form"

      I hope this helped you find the x-intercept and also why we only use y-intercept slope formulas.
      (6 votes)
  • blobby green style avatar for user hjjr62
    How do you find intercepts when the formula is more complex as in y=x*sqrt(16-x^2)
    (5 votes)
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  • aqualine ultimate style avatar for user FierceKat257
    So, if you wanted to do the same (figure out the x and y intercept) for any other equation, should I only use 0 as a substitute to figure them out? Would it be the same if you used other numbers as substitutes?
    (4 votes)
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    • hopper happy style avatar for user Rashel
      Katie, yes, exactly. If the equation is in standard form:ax+by=c then you just set x equal to 0 to find the y intercept and set y equal to 0 to find the x intercept. It makes sense, right. The y intercept is when the line crosses the y axis, so x will always be 0, so that is why we set x equal to 0. To find where the line crosses the y axis.

      The same logic applies when finding the x intercept, set y equal to 0 to find where the line crosses the x axis, because y will always be zero at the x intercept.
      Ex: (0,8) y intercept, notice x is 0
      (2,0) x intercept notice y is 0
      (5 votes)
  • blobby green style avatar for user waynemah95
    Need help, what do the "|" mean in an equation? Example, y=|x-2|
    Thanks
    (3 votes)
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  • leaf green style avatar for user Nikki
    How do answer questions about slope in word problems? That is my problem on math test with any unit.
    (4 votes)
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  • purple pi purple style avatar for user Anno Niem
    Is there a rule governing linear coordinates that pass the exact centre of the graph?
    For instance, where Xintercept=Yintercept=0...

    Since you can't draw a linear graph from using just one point, what can we do with such information?
    I understand a lot of formulas will meet with the centre, and the lines can angle 360degrees,
    through all quadrants of the graph when it does.
    But is it some type of typical linear graph? Or is there special methods involved?
    What can we know about situations that don't work while originally meeting the demands for the X/Yintercept method? (crossing both x0 and y0, being a linear equation etc.)
    Perhaps it is a singular exception?

    Sorry for this weakly translated and confusing question.
    I'd like to hear anything people got to say about this.
    (3 votes)
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    • leaf blue style avatar for user SteveG
      When linear coordinates pass the exact centre of the graph, i.e. x-int=y=int=0; you cannot draw a line just based off this information due to the fact that it is quintessential that you have or know a minimum of 2 points in order to graph the line. Factors of a line which will help in this scenario will include; the gradient, the equation of the line and even just simple another point. Hope this helps!
      (3 votes)
  • primosaur ultimate style avatar for user astro648
    Hello guys
    May I have some further explanation of figuring intercepts from charts and equations?
    Thank you
    (3 votes)
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  • primosaur seed style avatar for user NYC SUBWAY PRODUCTION
    Can X and Y be negative
    (2 votes)
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  • blobby green style avatar for user Drovensky R.
    how do you find the point of intersection for example of y= 3x + 2 and Y = 2x - -1
    (2 votes)
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  • blobby green style avatar for user erinreichert242
    How would i find the x-intercepts and y-intercepts (if they exist) of this function?
    f(x) = 2x2 + 21x + 40
    (2 votes)
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Video transcript

We're told to find the x- and y-intercepts for the graph of this equation: 2 y plus 1/3x is equal to 12. And just as a bit of a refresher, the x-intercept is the point on the graph that intersects the x-axis. So we're not above or below the x-axis, so our y value must be equal to 0. And by the exact same argument, the y-intercept occurs when we're not to the right or the left of the y-axis, so that's when x is equal to 0. So let's set each of these values to 0 and then solve for what the other one has to be at that point. So for the x-intercept, when y is equal to 0, let's solve this. So we get 2 times 0, plus 1/3x is equal to 12. I just set y is equal to 0 right there, right? I put 0 for y. Well, anything times 0 is just 0, so you're just left with 1/3x is equal to 12. To solve for x, you can think of it as either dividing both sides by 1/3, or we can multiply both sides by the reciprocal of 1/3. And the reciprocal of 1/3 is 3, or you can even think of it as 3 over 1. So times 3 over 1. And so we're left with 3 times 1/3, that just cancels out, so you're left with x is equal to 12 times 3, or x is equal to 36. So when y is equal to 0, x is 36. So the point 36 comma 0 is on the graph of this equation. And this is also the x-intercept. Now, let's do the same thing for the y-intercept. So let's set x equal 0, so you get 2y plus 1/3, times 0 is equal to 12. Once again, anything times 0 is 0. So that's 0, and you're just left with 2y is equal to 12. Divide both sides by 2 to solve for y, and you're left with y is equal to 12 over 2, is 6. So the y-intercept is when x is equal to 0 and y is equal to 6. So let's plot these two points. I'll just do a little hand-drawn graph, and make it clear what the x- and the y-intercepts are. So let me draw-- that's my vertical axis, and that is my horizontal axis-- and we have the point 36 comma 0. So this is the origin right here, that's the x-axis, that's the y-axis. The point 36 comma 0 might be all the way over here. So that's the point 36 comma 0. And if that's 36, then the point 0, 6 might be right about there. So that's the point 0, 6. And the line will look something like this. I'm trying my best to draw a straight line. And notice where the line intercepted or intersected the y-axis, that's the y-intercept, x is 0, because we're not to the right or the left of it. Where the line intersected the x-axis, y is 0, because we're not above or below it.