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Intro to intercepts

Learn what x- and y-intercepts are.  The equations used in this video are y = 0.5x - 3 and 5x + 6y = 30.

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  • piceratops ultimate style avatar for user Red Monster
    what would happen if you were to add the Z axis to the graph and then do the math?
    (15 votes)
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  • blobby green style avatar for user mondlanamandy
    What is the solution to this system of linear equations:
    X+2y+3z=6
    X+3y=0
    y-z=0
    (10 votes)
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  • aqualine ultimate style avatar for user Victor Soto
    What if both x and y equal 1?
    (1 vote)
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    • leafers seedling style avatar for user Mystear Primal
      Then...I doubt it would be counted as an intercept, as it'll have a different point of intersecting either axis. But it doesn't matter on the coordinates as you have provided only one coordinate, as a linear equation requires two.

      Yes, the point is (1, 1), but then again, it's not a linear equation is it? It's a coordinate. There are infinite linear equations where x=1 and y=1, so no concrete answers on the basis of intercepts.

      EDIT: Oops, didn't notice that it's a year old...
      (27 votes)
  • duskpin seedling style avatar for user gp728529
    How can you find the slope of a line like how can you find the answer of a line or a slope
    (10 votes)
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  • aqualine seed style avatar for user sitaramkarki
    y=-X^3 9
    how do we find the x and y intercepts?
    (5 votes)
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  • blobby green style avatar for user j.webster2273
    How do you find the intercepts from a graph
    (6 votes)
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  • male robot johnny style avatar for user grimdadeathdealer
    what is the formula for this?
    (4 votes)
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  • female robot ada style avatar for user Samantha
    I don't understand how to find x and y-intercepst. Like how to find say, an x-intercept of an linear equation. Or y-intercept of an equation. For example, how do you find the intercept of 4x-2=8?
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      4x-2=8 is a special type of linear equation.
      Start by simplifying the equation. Solve it so your equation looks like "X = a number"
      You will then have a linear equation where every point on the line will have an X-value equal to that number. For example: X=5 means X=5 for every possible value of Y that you can think of. So, you can have ordered pairs of: (5, 6); (5, 0); (5, -2); (5, -3.5); etc.
      If you graph them, you will see that this type of equation creates a vertical line. It has an X-intercept, but it does not have a Y-intercept (the vertical line never crosses the Y-axis).
      Hope this helps.
      (6 votes)
  • aqualine seed style avatar for user mmilam
    where did he get the 2 from when he multiplied it by 1/2
    (4 votes)
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  • aqualine sapling style avatar for user notahuman
    can a linear graph not have x- and y-intercepts?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      If the linear equation has two variables (X and Y), then it will have both an x-intercept and a y-intercept. They can turn out to be one point if the line happens to go thru the origin (0,0).

      If the linear equation is of the form: X = a number, then it is a vertical line and it has an x-intercept, but no y-intercept.

      If the linear equation is of the form: Y = a number, then it is a horizontal line and it has a y-intercept, but no x-intercept.

      Hope this helps.
      (5 votes)

Video transcript

- [Voiceover] Let's say that we have the linear equation, y = 1/2x - 3. So if we wanted to draw the line that represents the set of all points, all the coordinates where the x value and the y value satisfy this equation, we could start off by just trying to draw, by trying to draw a few of those points, and then connecting them with a line. Let's set up a little table here x, y. And we can just try a couple of x values here, then figure out what the corresponding y values are. I'm going to pick x values where it's going to be fairly easy to calculate the y values. Let's say when x is equal to zero, then you're gonna have 1/2 x 0 - 3, well then y is going to be -3. When x is, let me try x = 2, because then 1/2 x 2 is just gonna be 1. So when x = 2, you're going to have 1/2 x 2 = 1, -3 is -2. When x is equal to, let's try 4. So 1/2 x 4 is 2, and then -3 is -1, and we could keep going but actually all we need is two points for a line. So we're ready to plot this line if we'd like. The point 0, -3 is on this line. 0, -3 and actually let me do this in a slightly darker color so that we can see it on this white background. 0, -3 is on the line, 2, -2 is on the line. So 2, -2 and then we have 4, -1. So when x is 4, y is -1, and I could draw a line that connects all of these so it would look something like... If I, let's see if I could do this. It would look something like, it would something like, like that. So this right over here, this is literally, this is the graph of y = 1/2x - 3. Now when we look at a graph like this an interesting thing that we might want to ask ourself is where does the graph intersect our axes? So first we can say, well where does in intersect our x-axis? When you look at this, it looks like it happens at this point right over here. This point where a graph intersects an axes this is called an intercept. This one in particular is called the x-intercept. Why is it called the x-intercept? Because that's where the graph is intersecting the x-axis and the x-intercept, it looks like this is at the .6, 0. Now it's very interesting, the x-intercept happens when y = 0. Remember, you're on the x-axis when you haven't moved up or down from that axis which means y = 0. So your x-intercept happens at x = 6, y = 0. It's this coordinate. Now what about the y-intercept? Well the y-intercept is this point right over here. This is where you intersect or I guess you could say intercept the y-axis. So this right over here, that over there is the y-intercept. The y-intercept is at the coordinate that has a 0 for the x-coordinate. X is 0 here and y is -3. X is 0 and y is -3. This was actually one of the points, or one of the pairs that we first tried out. You can validate that 6, 0 satisfies this equation right over here. If x is 6, 1/2 x 6 is 3, -3 is indeed equal to 0. So now that we know what an x-intercept is, it's the point where a graph intersects the x-axis or intercepts the x-axis and the y-intercept is the point where a graph intercepts the y-axis or intersects the y-axis. Let's try to see if we can find the x and y-intercepts for a few other linear equations. So let's say that I had the linear equation. Let's say that I have 5x + 6y = 30. I encourage you to pause this video, and figure out what are the x and y-intercepts for the graph that represents the solutions, all the xy pairs that satisfy this equation. Well the easiest thing to do here, let's see what the y value is when x = 0 and what x value is when y = 0. When x = 0 this becomes 6y = 30. So 6 times what is 30? Well y would be equal to 5 here. So when x is 0, y is 5. What about when y is 0? Well when y is 0, that's going to be 0, and you have 5x = 30. Well then x would be equal to 6. Then x would be equal to 6. So we could plot those points, 0, 5. When x is 0, y is 5. When x is 6, y is 0. So those are both points on this graph and then the actual graph is going to, or the actual line that represents the x and y pairs that satisfy this equation is going to look like, it's going to look like this. I'll just try. So I can make it go, it's going to look like... It's going to go through those two points. So it going to...I can make it go the other way too. Let me see. It's going to go through those two points and so it's going to look something like that. Now what are its' x and y-intercepts? Well, we already kind of figured it out but the intercepts themselves, these are the points on the graph where they intersect the axes. So this right over here, this is the y-intercept. That point is the y-intercept and it happens, it's always going to happen when x = 0, and when x = 0 we know that y = 5. It's that point, the point 0, 5. And what is the y inter...what is the x-intercept? The x-intercept is the point, it's actually the same x-intercept for this equation right over here. It's the point 6, 0. That point right over there.