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Intercepts from an equation

Sal finds the x and y-intercepts of -5x + 4y = 20. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • leaf blue style avatar for user Lily Busse
    I am a 7th grader in Algebra I and we just started intercepts. One of the questions we had to answer was, Find an equation for the line described has x intercept 2 and y intercept 5. how would you do that?
    (103 votes)
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    • aqualine ultimate style avatar for user wanjuguam
      The points of the intecepts are (2,0) and (0,5). to find the equation of the line, you need to put it into slope-intercept form which is y=mx+b, where m is the slope and b is the y intercept. to find the slope you do 5-0 where you subtract the second y (5) from the first y (0). you put that over 0-2, where you subtract the first x (2) from the second x (0). your slope should look like this 5/-2.
      once you have your slope your equation should look like this,
      y=5/-2+b. to find b, you just put in the y intercept. the equation is
      y=5/-2+5
      (81 votes)
  • starky sapling style avatar for user blanabas
    I'm a little confused I attempted this question from the next practice section:

    Determine the intercepts of the line.
    −4x+7=2y-3

    And I came up with y= (0, -5) x= (2.5, 0)

    and when I entered my answer it told me it was incorrect and I looked at the hint and it seems like they wanted the same coordinates just with positive numbers instead.

    Is there a reason for that, for instance if I were taking the TASC do you think they'd accept my answer as well?

    I remember reading there is basically an infinite amount of answers for Linear Equations, I'm just curious as to if I computed it on my own wrong or just an awkward way.

    I did this:

    -4x+7=2y-3
    -7 -7

    -4x = 2y -10

    then

    4(0) = 2y = 10

    -10/2y = -5

    y = -5

    and

    -10/-4 = 2.5

    Sorry for the awful formatting my keyboard/ computer is all but completely broken
    (15 votes)
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    • male robot donald style avatar for user TheLuckyRobot
      -10/2y = -5
      When you're dividing, you don't reverse the sign. It should be
      2y - 10 = 0
      +10 to both sides
      2y = 10
      divide both sides by positive 2 (because the sign doesn't change as we're dividing)
      y = 10/2
      and finally:
      y = 5

      Any other questions? Feel free to comment me back!
      (12 votes)
  • leafers seed style avatar for user SoullessFire
    is Y always = to 0?
    (15 votes)
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  • blobby green style avatar for user Howard Mellow
    My question is more from experience. I am a 70 year old, taking this for a refresher. I know I have the right answer since I have attended a university in the field Electrical Engineering and Computer Science. However, I didn't get the problem right or wrong. The problem is how the computer accepts the answer. Do I have to enter the answer as a decimal, or a fraction? Please help since neither answer gave me the correct solutiopn. i.e. 3/4, 6/8, .75
    (9 votes)
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  • starky sapling style avatar for user ponyog
    What if you have a repeating decimal in your intercept? What can you do to avoid it?
    (8 votes)
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    • stelly blue style avatar for user Kim Seidel
      An intercept can be any real number: an integer, a fraction, a mixed number, a decimal.
      In the case of a repeating decimal, I would keep the number as a fraction rather than changing to a decimal. It's an easy way to keep the entire value of the intercept.
      (11 votes)
  • male robot donald style avatar for user T Reddy
    I am unsure whether there is a quicker way to find out the intercepts. I know that if you have a line equation that is like
    y=2x+3 that the y-intercept is (0,3)
    But is there a quick way for the x-intercept like this with any particular types of linear equations?
    (8 votes)
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    • male robot hal style avatar for user Curtis.Barville
      There may be a faster way, but it is fairly quick and certain when you begin the y-intercept (0,3) and plot points based on the slope [rise 2, run 1 => (1, 5), (2, 7) or reverse (-1, 1), (-2, -1)].
      I usually plot three points and draw a line through them to find the x-intercept (-1.5, 0).
      (2 votes)
  • female robot grace style avatar for user Anna
    if the x intercept is 2 and the y intercept is -1 what is the slope of the corresponding line?
    (5 votes)
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  • female robot grace style avatar for user Faithy
    What is the importance of an x or y intercepts ?
    (6 votes)
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  • starky tree style avatar for user hernande.agustin647
    I am a 9th grader at Whittier high school doing algebra 1, we are reviewing how to get Intercepts from an equation. One of the questions given is a little confusing for me and a few of my classmates. How would I get the X and Y intercepts from this? y−6=4(x+5)
    (2 votes)
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    • starky sapling style avatar for user KC
      To get the X intercept plug in 0 for y so: 0-6=4(x+5)
      Then solve for x the x intercept will be (-6.5, 0)
      To get the Y intercept plug in 0 for x so: y-6=4(0+5)
      then solve for y, the y interpect will be (0, 26)
      I'm pretty sure, I hope this makes sense I can explain it in more depth if necessary.
      (11 votes)
  • leaf green style avatar for user joeasanchez1223
    how do you know if the intercept you found is right? And why do we have to put the answer as an irrational? and how do we know when to put it as an irrational?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      You can always plug in the point to see if it works in the equation. So with -5x+4y=20, you have an x intercept of (-4,0) and -5(-4)+4(0)=20 gives 20=20, so it is correct. With (0,5), -5(0)+4(5)=20 also gives 20=20, so they work.
      I am not sure what you mean by having the answer as an irrational number in linear equations. Almost all linear equations will have rational solutions especially what you deal with in Algebra I. It is more likely to get irrational solutions when you are talking about quadratic equations.
      (4 votes)

Video transcript

We have the equation negative 5x plus 4y is equal to 20, and we're told to find the intercepts of this equation. So we have to find the intercepts and then use the intercepts to graph this line on the coordinate plane. So then graph the line. So whenever someone talks about intercepts, they're talking about where you're intersecting the x and the y-axes. So let me label my axes here, so this is the x-axis and that is the y-axis there. And when I intersect the x-axis, what's going on? What is my y value when I'm at the x-axis? Well, my y value is 0, I'm not above or below the x-axis. Let me write this down. The x-intercept is when y is equal to 0, right? And then by that same argument, what's the y-intercept? Well, if I'm somewhere along the y-axis, what's my x value? Well, I'm not to the right or the left, so my x value has to be 0, so the y-intercept occurs when x is equal to 0. So to figure out the intercepts, let's set y equal to 0 in this equation and solve for x, and then let's set x is equal to 0 and then solve for y. So when y is equal to 0, what does this equation become? I'll do it in orange. You get negative 5x plus 4y. Well we're saying y is 0, so 4 times 0 is equal to 20. 4 times 0 is just 0, so we can just not write that. So let me just rewrite it. So we have negative 5x is equal to 20. We can divide both sides of this equation by negative 5. The negative 5 cancel out, that was the whole point behind dividing by negative 5, and we get x is equal to 20 divided by negative 5 is negative 4. So when y is equal to 0, we saw that right there, x is equal to negative 4. Or if we wanted to plot that point, we always put the x coordinate first, so that would be the point negative 4 comma 0. So let me graph that. So if we go 1, 2, 3, 4. That's a negative 4. And then the y value is just 0, so that point is right over there. That is the x-intercept, y is 0, x is negative 4. Notice we're intersecting the x-axis. Now let's do the exact same thing for the y-intercept. Let's set x equal to 0, so if we set x is equal to 0, we have negative 5 times 0 plus 4y is equal to 20. Well, anything times 0 is 0, so we can just put that out of the way. And remember, this was setting x is equal to 0, we're doing the y-intercept now. So this just simplifies to 4y is equal to 20. We can divide both sides of this equation by 4 to get rid of this 4 right there, and you get y is equal to 20 over 4, which is 5. So when x is equal to 0, y is equal to 5. So the point 0, 5 is on the graph for this line. So 0, 5. x is 0 and y is 1, 2, 3, 4, 5, right over there. And notice, when x is 0, we're right on the y-axis, this is our y-intercept right over there. And if we graph the line, all you need is two points to graph any line, so we just have to connect the dots and that is our line. So let me connect the dots, trying my best to draw as straight of a line is I can-- well, I can do a better job than that-- to draw as straight of a line as I can. And that's the graph of this equation using the x-intercept and the y-intercept.