If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Intercepts from a table

Sal finds the y-intercept of the graph of a linear function given a table of values. Created by Sal Khan.

Want to join the conversation?

  • duskpin tree style avatar for user Grace Domingo
    The thing is, it's easy to understand here, but when you actually start the practice, it's totally different.
    (85 votes)
    Default Khan Academy avatar avatar for user
  • spunky sam blue style avatar for user Albert Chhab
    What is function? We did not learn about it yet.
    (21 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Divija R
    Is there any way to find intercept x ( or y) if we cannot get the other intercept to zero by following the table method?
    In all the questions, if we need to find intercept x/y, the other intercept always perfectly reaches to zero.
    (5 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Hecretary Bird
      If the table doesn't directly go to 0, you could always get the equation of the line described by the table and then plug in 0 for x to get the y-int, or 0 for y to get x-int. To get the equation of a line from a table, you need to determine the slope of the line by calculating the ratio of the change in y-value to the change in x-value. For example, if two points in the table were (1, 2) and (4, 8), you could see that the y value changed by 6 and the x value changed by 3. This would give you a slope of 2 through 6 / 3 = 2. You can then plug a data set for a point into the linear slope-intercept equation: y = mx + b. Going with the numbers from the previous example, let's say I plugged in (1,2). Since m is the slope, my equation would look a little something like this:
      2 = 2*1 + b
      From there, we can solve for b, and see that b = 0:
      2 = 2 + b
      2 - 2 = 2 + b - 2
      0 = b
      Since b is 0, our completed equation looks like this:
      y = 2x + 0
      To find the intercepts of this equation, we just substitute a 0 in the right place. To find the y-intercept, plug in a 0 for x:
      y = 2*0 + 0
      y = 0
      And for the x-intercept:
      0 = 2x + 0
      0/2 = 2x/2
      0 = x

      Hope this helped!
      (24 votes)
  • aqualine ultimate style avatar for user katherine
    What if there is a straight line and it never passes through one of the axis? Just curious.
    (2 votes)
    Default Khan Academy avatar avatar for user
  • female robot ada style avatar for user sarnow7294
    Why is it when the line crosses y it is the y-intercept?? why dont we just call it "the time the line crosses the y-axis?"
    (2 votes)
    Default Khan Academy avatar avatar for user
  • female robot grace style avatar for user masad
    so what about the x- intercept also that is being asked in the practice intercept from a table......
    (6 votes)
    Default Khan Academy avatar avatar for user
  • winston baby style avatar for user Misho Totaresku
    i am confused at . why does the -1/2 mean?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • sneak peak blue style avatar for user Stephen Earley
    What if your table is going down (or up) by a number that will miss zero?
    If I have, say, 8 on the x side, but my table is decreasing every 15, then my next input would miss zero and go to -5! What do I do there?

    This is implying that the other side cannot be divided by said number.
    (5 votes)
    Default Khan Academy avatar avatar for user
  • leafers tree style avatar for user Arshiya Hasan
    How do you find the x and y intercepts with just random coordinates they give you? For example, they gave me (-15, 5), (-9, 10), and (-3, 15). That's all they gave me! Those are random coordinates to a line! Am I supposed to fill in the blanks myself??
    (3 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Saivishnu Tulugu
      In reality, you only need 2 of these points. The first step is to find the slope which is (y2-y1)/(x2-x1) and you can use any of these points. Next write the equation is point slope form which is y-y1=m(x-x1) using the slope and one of the points. Then you can simplify to write this is slope-intercept form and solve the x and y intercepts as given. Remember these coordinates are not random as they are all on the same line!
      (4 votes)
  • starky seedling style avatar for user CastellanosCole
    Why is it that the intercept is 4 instead of -2?
    (4 votes)
    Default Khan Academy avatar avatar for user

Video transcript

The following table of values represents points x comma y on the graph of a linear function. Determine the y-intercept of this graph. So just as a reminder of what the y-intercept even is, if you imagine a linear function or a line if we're graphing it, if we imagine a line, so let's say that is our line right over there. This is our y-axis. This is our x-axis. The y-intercept is where we intersect the y-axis. Now, what do we know about the y-intercept? Well, at the y-intercept x is going to be equal to 0. So this is the point 0 comma something. And so when people are talking about, what is your y-intercept? They're usually saying, well, what is the y-coordinate when x equals 0. So we're really trying to figure out, what is the y-coordinate when x equals 0? So we know the x-coordinate when y is equal to 0. So this is actually the x-intercept. So this point right over here is the point 2 comma 0. So when people say x-intercept, that's the x-coordinate when y equals 0. Well, they gave us the x-intercept. So that right over there is the x-intercept. But what's the y-intercept? What is the y-value when x equals 0? Well, let's see. They give us what happens to y when x is negative 2, when it's 1, when it's 2, when it's 4. So maybe we can backtrack from one of these to get back to what happens when x is equal to 0. So let me rewrite this table so I can give ourselves a little bit more breathing room. So let's say we have x and we have y. x and y. And they already tell us that when x is negative 2, y is 8. And I actually want to think about what happens when x is negative 1, when x is 0. Then they tell us when x is 1, y is 2. When x is 2, y is 0. This right over here is the x-intercept. When x is 4, y is negative 4. So they skip 2 right over here. y is negative 4. So let's just see how y changes with respect to changes in x. So when we go here, when x changes by 1, y goes down by 2. And it's a line, so it's going to have a constant rate of change of y with respect to x. So similarly, when x increases by 1, y is going to decrease by 2. So y is going to be 6 here. When x increases by 1 again, y is going to decrease by 2. So we're going to get to 4. And we see it works. Because if we increase by 1 again, then it is indeed the case that y decreased by 2. And you see here when we increase x by 2, then y decreases at twice the rate. Because now we didn't just increase by 1, we increased by 2. So now y is going to decrease by 4. And what's constant here is your change in y over your change in x. When x increases by 1, y decreases by 2. When x increases by 2, y decreases by 4. Either way you think about it, your change in y for a unit change in x is going to be equal to negative 2. But anyway, we actually answered the question before without even realizing it when we filled in all of these values. What is the y-value when x equals 0? Well, the y-value is 4. So the y-intercept here is 4. We didn't really graph this to scale. It would actually look a little bit more like this if we were to try to graph it properly. So this right over here is 4. This right over here is 2. And our line looks something like this. Our line will look something like that.