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x-intercept of a line

Sal determines the x-intercept of a linear equation from a graph. Afterwards, he checks his work by plugging values back into the equation. Created by Sal Khan.

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  • aqualine ultimate style avatar for user retrest
    How do you find the y intercept?
    (12 votes)
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    • male robot donald style avatar for user michael Li
      You can take the function f(x) = something (your funtion) so like f(x)=2x. you can input x=0 and find the output which would be the y intercept. So, lets actually have f(x) = 5x + 2. You input 0 for x and you get f(x) = 2. That is your y intercept
      (13 votes)
  • starky tree style avatar for user Ani-Jay
    How do you know where to put your intercepts when answering the problems.? I haven't been able to get 100% on the practice problems, because my answers need to be reversed, but I can't figure out where to place them.
    (10 votes)
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  • duskpin ultimate style avatar for user Sara Beth
    Can't you find the intercept by doing -b/2a, or is that finding the vertex?
    (5 votes)
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    • leafers ultimate style avatar for user KathyC
      A vertex is a corner, where two lines meet. A straight line by itself doesn't have a vertex.

      The easiest way to find the x intercept is to figure out what value x will have when y = 0.
      So if you have an equation of a line: 2y + 4x = 28
      you substitue "0" in for your y and solve:
      2 (0) + 4x = 28
      4x = 28
      x = 7
      The x intercept is (7,0)
      (8 votes)
  • leaf green style avatar for user AshwathMalaisamy
    for example how would you find the x intercept for a problem like this ?Y = x2 + 5x + 4
    y = x squared plus five x plus four
    (5 votes)
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    • hopper happy style avatar for user Rashel
      It's a quadratic equation, which means it's a non-linear (is parabolic in shape). You can find the x-intercepts (usually there are 2, but there can be 1 or none) by completing the square, factoring or by using the quadratic formula. Which method I use depends on which one I think will make solving the problem easier. The easiest way to solve is to factor the quadratic equation.
      x^2+5x+4=0

      We set it equal to zero because we are looking for the x intercepts.
      When y is 0 where will the parabola cross the x-axis

      To solve by factoring we ask ourselves: What two numbers add up to the middle term and are the product of the last term?
      4*1=4 (last term)
      4+1=5 (middle term)
      (x+4) (x+1)
      set them both equal to zero to find the x intercept
      x+4=0
      subtract 4 from both sides
      x=-4
      x+1=0
      subtract 1 from both sides
      x=-1
      x intercepts are -4 and -1. Or the points where the parabola crosses the x-axis are (-4,0) and (-1,0).
      (7 votes)
  • blobby green style avatar for user Ammon Trump
    How would I find the x and y intercepts and graph them if I have a function 3x - 5y=15
    (6 votes)
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  • spunky sam orange style avatar for user daP0l15hc0unt
    Slope intercept form is y=mx+b.
    Is there a way to use the x-intercept instead of the y-intercept. Use p for the y-intercept in your equation.

    My attempt:
    y = mx + b
    0 = mx + b
    0 = x + b/m
    x = -b/m
    let p be the x-intercept
    therefore: p = -b/m
    Therefore:y = mx - mp
    Am I right?
    (4 votes)
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  • leaf green style avatar for user Eliza Laycock
    What is a slope?
    (3 votes)
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  • piceratops ultimate style avatar for user Nakulisthebest
    I have a question what is the equation of x intercept?
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      There is no equation. You take the linear equation that you have and you replace Y with 0. Then, solve for X. You will have a point on the line at (x-value, 0) where the x-value is the value you found. This point is where the line cross the x-axis (so, it is the x-intercept).
      (2 votes)
  • blobby green style avatar for user dev pareek
    how to find x intercept when y= -x^2+16
    (3 votes)
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  • eggleston blue style avatar for user Killian, Carly
    how would you find the x intercept of 2x-y= 5?
    (3 votes)
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Video transcript

The graph of the line 2y plus 3x equals 7 is given right over here. Determine its x-intercept. The x-intercept is the x value when y is equal to 0, or it's the x value where our graph actually intersects the x-axis. Notice right over here our y value is exactly 0. We're sitting on the x-axis. So let's think about what this x value must be. Well, just trying to eyeball a little bit, it's a little over 2. It's between 2 and 3. It looks like it's less than 2 and 1/2. But we don't know the exact value. So let's go turn to the equation to figure out the exact value. We essentially have to figure out what x value, when y is equal to 0, will have this equation be true. So we could just say 2 times 0 plus 3x is equal to 7. Well, 2 times 0 is just going to be 0, so we have 3x is equal to 7. Then we can divide both sides by 3 to solve for x, and we get x is equal to 7/3. Does that look like 7/3? Well, we just have to remind ourselves that 7/3 is the same thing as 6/3 plus 1/3. And 6/3 is 2. So this is the same thing as 2 and 1/3. Another way you could think about it is 3 goes into 7 two times, and then you have a remainder of 1. So you've still got to divide that 1 by 3. It's 2 full times and then a 1/3, so this looks like 2 and 1/3. And so that's its x-intercept, 7/3. If I was doing this on the exercise on Khan Academy, it's always a little easier to type in the improper fraction, so I would put in 7/3.