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Determining Intercepts

Determining Intercepts

Author: Colleen Atakpu
Description:

This lesson demonstrates how to determine intercepts.

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Today we're going to talk about how to find the x- and y-intercepts of a line. Remember the x- and y-intercepts are just where a line crosses the x-axis and the y-axis on a graph. So we're going to do some examples of finding the x- and y-intercepts first from a graph, then from a table, and finally from an equation.

So let's look at how to find the x- and y-intercepts by looking at a graph. So here's a graph of a line, and I see that it intersects my x-axis at x equals 2, and my y-axis at y equals 5. So the y-intercept, remember, can be defined as the place where the line intersects the y-axis, and similarly the x-intercept is where our line intersects with the x-axis.

So our y-intercept has the point 0, 5, again because my x-coordinate of this point is 0 and my y-coordinate of this point is 5. And so you can also think of the y-intercept as the value of y when x is equal to 0.

So similarly for our x-intercept, the x-intercept is where our line is going to intersect with the x-axis. And so here, this point has the coordinates 2, 0 because my x-coordinate at this point is 2 and my y-coordinate at this point is 0. So I can also again think of the x-intercept as the value of x when y is equal to 0.

So let's look at how to find our x- and y-intercepts by looking at a table of values.

So let's look at how to find the x- and y-intercepts of a line by looking at a table of its x and y values.

So remember that the y-intercept is the value of y when x is equal to 0. So if I look in my table for when x is equal to 0, I see that the value of y when x is equal to 0 is just 8. So on a graph, the point 0, 8 is going to be my y-intercept.

And similarly, the x-intercept is the value of x when y is equal to 0. So looking at my table I find that when y is 0, x is 2. So the point 2, 0 on my graph would be the x-intercept.

So lastly let's look at how you can find the x- and y-intercepts of a line if you only have an equation and don't have a graph to locate the intercepts.

So if I have an equation y equals negative 3x plus 6, again if I were to graph this on a coordinate plane, I would see that it forms a line like the other examples we've looked at. And so if I want to find the x-intercept, I know that the x-intercept is when y is equal to 0. So I can substitute 0 in for my y into the equation to figure out the value of x.

So substituting 0 in for y, my equation becomes 0 equals negative 3x plus 6. Since I want to find the value of x, I'm going to isolate the x variable. So I'll start by subtracting 6 on both sides to cancel this out. And I'm left with negative 3x is equal to negative 6.

Then I'm going to divide both sides by negative 3 to cancel out the negative 3 here, multiplying by the x. And that's going to give me x by itself on this side, negative 6 divided by negative 3 will give me 2. So I found that my x value when y is 0 is 2, which means that my x-intercept is at the point 2, 0.

I can also find my y-intercept by substituting 0 in for x because I know that my y-intercept is the value of y when x is equal to 0. So substituting 0 into my equation, this becomes y equals negative 3 times 0 plus 6. Simplifying this because I already have my y variable isolated by itself-- negative three times 0 is just going to give me 0. And 0 plus 6 is just going to give me 6. So I found that the value of y is 6 when x is equal to 0, so that means that my y-intercept is at the point 0, 6.

So let's go over our key points from today. As usual, make sure you have them in your notes if you don't already so you can refer to them later.

The x-intercept is where a line or a curve intersects the x-axis. It is also where y equals 0 and is written as x, 0 as a coordinate pair.

The y-intercept is where a line or curve intersects the y-axis. It is also where x equals 0 and is written as 0, y as a coordinate pair.

So I hope that these key points and examples helped you understand a little bit more about finding the x- and y-intercepts of a line. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.

Notes on "Determining Intercepts"

Key Terms

  • y-intercept: 
  • Where a line or curve intersects the y-axis, at x=0.
  • x-intercept: 
  • Where a line or curve intersects the x-axis, at y=0.

Key Formulas

None