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Every linear equation has a unique line that represents all the solutions of the equation. When graphing a line by plotting points, each person who graphs the line can choose any three points, so two people graphing the line might use different sets of points.

At first glance, their two lines might appear different since they would have different points labeled. But if all the work was done correctly, the lines will be exactly the same line. One way to recognize that they are indeed the same line is to focus on where the line crosses the axes. Each of these points is called an intercept of the line.

The intercepts of a line are the points where the line intercepts, or crosses, the horizontal and vertical axes. To help you remember what “intercept” means, think about the word “intersect.” The two words sound alike and in this case mean the same thing.

Table of Contents

## Identify the [latex]x[/latex]- and [latex]y[/latex]- Intercepts From a Graph

The straight line on the graph below intercepts the two coordinate axes. The point where the line crosses the *x*-axis is called the [latex]x[/latex]-intercept. The [latex]y[/latex]-intercept is the point where the line crosses the *y*-axis.

In the graph above, the x-intercept occurs when [latex]x=-2[/latex] and the y-intercept occurs when [latex]y=2[/latex]. We typically express the intercepts by giving the ordered pair, so we say that the *x*-intercept above is at the point [latex](−2,0)[/latex] and the *y*-intercept above is at the point [latex](0, 2)[/latex].

Notice that the intercept always occurs where [latex]x=0[/latex], and the *x*-intercept always occurs where [latex]y=0[/latex].

Let’s look at the graph of the lines shown below.

First, notice where each of these lines crosses the x- axis:

**Figure:** **The line crosses the x-axis at:** **Ordered pair of this point** [latex]a[/latex] [latex]3[/latex] [latex](3,0)[/latex] [latex]b[/latex] [latex]4[/latex] [latex](4,0)[/latex] [latex]c[/latex] [latex]5[/latex] [latex](5,0)[/latex] [latex]d[/latex] [latex]0[/latex] [latex](0,0)[/latex]

Do you see a pattern?

For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs when y is zero.

Now, let’s look at the points where these lines cross the y-axis.

**Figure:** **The line crosses the y-axis at:** **Ordered pair for this point** [latex]a[/latex] [latex]6[/latex] [latex](0,6)[/latex] [latex]b[/latex] [latex]-3[/latex] [latex](0,-3)[/latex] [latex]c[/latex] [latex]-5[/latex] [latex](0,-5)[/latex] [latex]d[/latex] [latex]0[/latex] [latex](0,0)[/latex]

In the following video, we provide another example of how to find the intercepts of a line from a graph.

## Find the Intercepts From an Equation of a Line

Recognizing that the [latex]xtext{-intercept}[/latex] occurs when [latex]y[/latex] is zero and that the [latex]ytext{-intercept}[/latex] occurs when [latex]x[/latex] is zero gives us a method to find the intercepts of a line from its equation.

For example, the linear equation [latex]3y+2x=6[/latex] has an *x* intercept when [latex]y=0[/latex], so [latex]3left(0right)+2x=6[/latex].

[latex]begin{array}{r}2x=6\x=3end{array}[/latex]

The x-intercept is [latex](3,0)[/latex].

Likewise the *y*-intercept occurs when [latex]x=0[/latex].

[latex]begin{array}{r}3y+2left(0right)=6\3y=6\y=2end{array}[/latex]

The *y*-intercept is [latex](0,2)[/latex].

In the following example we show you how to find the intercepts of a line given in a different form than the examples above.

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## Top 14 what are the intercepts edit by Top Q&A

### Y Intercept Definition (Illustrated Mathematics Dictionary) – Math is Fun

**Author:**mathsisfun.com**Published Date:**07/03/2022**Review:**4.83 (980 vote)**Summary:**Illustrated definition of Y Intercept: The point where a line or curve crosses the y-axis of a graph. We can often find it by setting x to zero and…

### Finding the x-intercepts of a function – Math Bootcamps

**Author:**mathbootcamps.com**Published Date:**12/04/2022**Review:**4.64 (347 vote)**Summary:**Lesson covering the definition of an x-intercept and examples of how to find the x-intercepts of a function using a graph or using algebra.

### Intercepts of a Linear Equation

**Author:**columbia.edu**Published Date:**03/20/2022**Review:**4.24 (337 vote)**Summary:**Intercepts of a Linear Equation ; x intercept, The x intercept is the point where the line crosses the x axis. At this point y = 0. ; y intercept, The y intercept …**Matching search results:**For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs …

### What’s the Y-Intercept? | Virtual Nerd

**Author:**virtualnerd.com**Published Date:**01/19/2023**Review:**4.05 (352 vote)**Summary:**Note: When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis. In this tutorial, learn about the …**Matching search results:**For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs …

### x – and y -Intercepts

**Author:**purplemath.com**Published Date:**07/10/2022**Review:**3.83 (539 vote)**Summary:**Intercepts are places where a graph crosses, or at least touches, an axis. An x-intercept is where the graph crosses (or touches) the x-axis; a y-intercept …**Matching search results:**For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs …

### Y-Intercepts – Varsity Tutors

**Author:**varsitytutors.com**Published Date:**09/12/2022**Review:**3.72 (342 vote)**Summary:**The y-intercept of a function is the point(s) where the graph of the function crosses the y-axis.**Matching search results:**For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs …

### Determining the Meaning of Intercepts

**Author:**texasgateway.org**Published Date:**01/05/2023**Review:**3.4 (594 vote)**Summary:**Determining and Interpreting Intercepts from an Equation. Linear equations can be written in two forms. Slope-Intercept Form, Standard Form …**Matching search results:**For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form [latex]left(a,0right)[/latex] ; and is called the x-intercept of the line. The x-intercept occurs …

### Intercepts of Linear Equations

**Author:**content.nroc.org**Published Date:**12/25/2022**Review:**3.33 (330 vote)**Summary:**The intercepts of a line are the points where the line intercepts, or crosses, the horizontal and vertical axes. The straight line on the graph below …**Matching search results:**To find the y-intercept, we substitute 0 for x in the equation, because we know that every point on the y-axis has an x-coordinate of 0. Once we do that, we can solve to find the value of y. When we make x = 0, the equation becomes , which works out …

### Finding x-intercepts and y-intercepts | College Algebra | | Course Hero

**Author:**coursehero.com**Published Date:**05/31/2022**Review:**3.03 (472 vote)**Summary:**The intercepts of a graph are points at which the graph crosses the axes. … To determine the x-intercept, we set y equal to zero and solve for x.**Matching search results:**To find the y-intercept, we substitute 0 for x in the equation, because we know that every point on the y-axis has an x-coordinate of 0. Once we do that, we can solve to find the value of y. When we make x = 0, the equation becomes , which works out …

### 3.3: Graph Using Intercepts – Mathematics LibreTexts

**Author:**math.libretexts.org**Published Date:**03/06/2022**Review:**2.99 (182 vote)**Summary:**Hence the y-intercept is (0,6). Note that this linear equation is graphed above. Answer: x-intercept: ( …**Matching search results:**To find the y-intercept, we substitute 0 for x in the equation, because we know that every point on the y-axis has an x-coordinate of 0. Once we do that, we can solve to find the value of y. When we make x = 0, the equation becomes , which works out …

### Intro to intercepts (video) – Khan Academy

**Author:**khanacademy.org**Published Date:**11/22/2022**Review:**2.73 (97 vote)**Summary:**So now that we know what an x-intercept is, it’s the point where a graph intersects the x-axis …

Dauer:

Gepostet:**Matching search results:**To find the y-intercept, we substitute 0 for x in the equation, because we know that every point on the y-axis has an x-coordinate of 0. Once we do that, we can solve to find the value of y. When we make x = 0, the equation becomes , which works out …

### X Intercept – Calculate, How to Find X Intercept on a Graph? – Cuemath

**Author:**cuemath.com**Published Date:**04/24/2022**Review:**2.68 (168 vote)**Summary:**the x-intercept is also known as horizontal intercept. X Intercept Formula. There are various formulas and equations associated with intercepts. Below listed …**Matching search results:**In the linear equation, we read that the general form is represented as y = mx + b, where m and b are constants. The x-intercept is the point or the coordinate from where the line crosses and that lies at the x-axis of the plane. This means the …

### Find the X and Y Intercepts of a Line Using Algebra

**Author:**content.byui.edu**Published Date:**03/25/2022**Review:**2.67 (150 vote)**Summary:**To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b …**Matching search results:**In the linear equation, we read that the general form is represented as y = mx + b, where m and b are constants. The x-intercept is the point or the coordinate from where the line crosses and that lies at the x-axis of the plane. This means the …

### Intercepts of a Function Equation & Graph | How to Find X & Y

**Author:**study.com**Published Date:**03/22/2022**Review:**2.44 (153 vote)**Summary:**Linear functions create straight lines on graphs. Linear functions are defined algebraically by slope-intercept form f( …**Matching search results:**In the linear equation, we read that the general form is represented as y = mx + b, where m and b are constants. The x-intercept is the point or the coordinate from where the line crosses and that lies at the x-axis of the plane. This means the …