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Determining Intercepts

Determining Intercepts

Author: Anthony Varela
Description:

Determine the x-intercept and y-intercept of an linear equation.

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Hi. This is Anthony Varela, and this tutorial is about determining intercepts. So we're going to be determining intercepts from a graph of a line, we'll take a look at a table of values representing a line, and then we'll look at the equation of a line and find their intercepts. So what do I mean by intercepts? Well, I mean two kinds of intercepts.

The x-intercept is where a line or a curve intersects the y-axis, and this occurs at y equals 0. The y-intercept is where a line or a curve intersects the y-axis, and this is at x equals 0. So taking a look at a coordinate plane, the x-intercept, then, is where anything crosses the x-axis, and notice that the x-axis is at y equals 0. Now, the y-intercept, then, is when anything crosses the y-axis, and you can see here that this is when x is 0.

So here's a very rough sketch of a line on a graph. And I've located their x and y-intercepts. So here's the x-intercept. It has some coordinates. X-coordinate value, I don't quite know, but I do know that y is 0. For the y-intercept, I know that the x-coordinate is 0, and then the y-coordinate, I don't quite know.

So for x-intercepts, it intersects the x-axis. It's at y equals 0, so its general coordinate is x, comma, 0. For y-intercepts, it intersects the y-axis. It's at x equals 0, so its a general coordinate is 0, comma, y.

So let's go ahead, then, and identify x and y-intercepts from a graph of a line. So here, we see the graph of the line. And now you can see where it intersects the y and x-axes. So I'm going to mark those down. These are my x and y-intercepts.

So what are these coordinates? Well, the coordinate of the x-intercept is negative 3, 0. So it is the value of x when y equals 0. And that happens at x equals negative 3. For our y-intercept, the coordinate is 0, comma, 2. So it is the value of y when x equals 0. So that value would be y equals 2 when x equals 0.

We can also determine intercepts from a table of values. Remember, for the x-intercept, it's when y equals 0, and for the y-intercept, it's when x equals 0. So I'm going to look for values of 0 in my x column and my y column. So I'm going to go ahead and highlight. Here's one, and here's my other. Now, these represent coordinate pairs, and these are going to be either my x-intercepts or my y-intercepts.

Well, the x-intercept is the value of x when y equals 0, so that would be this coordinate right here. And then the y-intercept is the value of y when x equals 0, so here's x equals 0. Here's y equals 8. So these are my x and y-intercepts.

Once again, which one is which? This has to be the y-intercept, because it fits this form. And this has to be the x-intercept, because it fits this form.

Our last example has us determining intercepts from an equation. So unlike a graph, where we can look at where a certain point equals 0, or unlike a table, where we can locate those values of 0, from an equation, we just need to plug in values for 0 for either x or y and solve for the other variable. So to determine the x-intercept, remember, this is when y equals 0, so we're going to solve for x when y equals 0. And to find the y-intercept, we're going to solve for y when x equals 0.

So let's find the x-intercept. So I'm plugging in 0 for y. So I have 0 equals negative 3x plus 2, and I need to isolate x. So first, I'm going to subtract 2 from both sides to get negative 2 equals negative 3x. Then, I'll divide both sides by negative 3, so now I know that x equals 2/3. So my x-intercept is at 2/3, 0.

To find the y-intercept, I'm going to solve for y when x equals 0. So y equals negative 3 times 0 plus 2. Well, negative 3 times 0 is just 0, so I have y equals 0 plus 2, or y equals 2. So my y-intercept, then, is the coordinate point 0, 2.

So let's review determining intercepts. For the x-intercept, this intersects the x-axis. This occurs at y equals 0. It has the general coordinate x, comma, 0. The y-intercept intersects the y-axis. It is at x equals 0, so its general coordinate is 0, comma, y.

Thanks for watching this tutorial on determining intercepts. Hope to see you next time.

Terms to Know
x-intercept

the location on a graph where a line or curve intersects the x-axis: (x, 0)

y-intercept

the location on a graph where a line or curve intersects the y-axis: (0, y)