How to find the y intercept from a graph

Question

Background Tutorials

X- and Y-Intercepts
- Table of Contents Show
Working with Slope-Intercept Form
- What's Slope-Intercept Form of a Linear Equation?
  When you're learning about linear equations, you're bound to run into the point-slope form of a line. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. Watch this tutorial, and learn about the point-slope form of a line!
Ordered Pairs and The Coordinate Plane
- What is the X-Coordinate?
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair!
- What is the Y-Axis?
  To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the y-axis and see where it's located in the coordinate plane.

The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . )

The y -intercept is often referred to with just the y -value. For example, we say that the y -intercept of the line shown in the graph below is 3.5 .

When the equation of a line is written in slope-intercept form ( y = m x + b ), the y -intercept b can be read immediately from the equation.

Example 1:

The graph of y = 3 4 x − 2 has its y -intercept at − 2 .

Similarly, for a quadratic equation written in standard form y = a x 2 + b x + c , the y -intercept is c .

Example 2:

The graph of y = − x 2 − x + 3 has its y -intercept at 3 .

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.