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methods

1Using a Graph of a Line

2Using the Equation of the Line

3Using the Quadratic Formula

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Article Summary

**Co-authored by**David Jia

Last Updated: June 12, 2023Fact Checked

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In algebra, 2-dimensional coordinate graphs have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a range of values cross these axes are called intercepts. The y-intercept is the place where the line crosses the y-axis and the x-intercept where the line crosses the x-axis. For simple problems, it is easy to find the x-intercept by looking at a graph. You can find the exact point of the intercept by solving algebraically using the equation of the line.

Method 1

Method 1 of 3:

### Using a Graph of a Line

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1

**Identify the x-axis.**A coordinate graph has a y-axis and an x-axis. The x-axis is the horizontal line (the line that goes from left-to-right). The y-axis is the vertical line (the line that goes up and down).^{[1]}It is important to look at the x-axis when locating the x-intercept.2

**Find the point where the line crosses the x-axis.**The x-intercept is this point.^{[2]}If you are asked to find the x-intercept based on the graph, the point will likely be exact (for example, at point 4). Usually, however, you will have to estimate using this method (for example, the point is somewhere between 4 and 5).Advertisem*nt

3

**Write the ordered pair for the x-intercept.**An ordered pair is written in the form and gives you the coordinates for the point on the line.^{[3]}The first number of the pair is the point where the line crosses the x-axis (the x-intercept). The second number for will always be 0, since a point on the x-axis will never have a value for y.^{[4]}- For example, if a line crosses the x-axis at point 4, the ordered pair for the x-intercept is .

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Method 2

Method 2 of 3:

### Using the Equation of the Line

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1

**Determine that the equation of the line is in standard form.**The standard form of a linear equation is .^{[5]}In this form, , , and are integers, and and are the coordinates of a point on the line.- For example, you might be given the equation .

2

**Plug in 0 for .**The x-intercept is the point on the line where the line crosses the x-axis. At this point, the value for will be 0. So, in order to find the x-intercept, you need to set the to 0 and solve for .^{[6]}- For example, if you substitute 0 for , your equation will look like this: , which simplifies to .

3

**Solve for .**To do this, you need to isolate the x variable by dividing both sides of the equation by the coefficient. This will give you the value of when , which is the x-intercept.^{[7]}See Alsox-intercept of a line (video) | Khan AcademyIntercepts of lines review (x-intercepts and y-intercepts) (article) | Khan AcademyHow to Find X Intercept? Definition, Formula, Graph, Examples3.3: Graph Using Intercepts- For example:

- For example:
4

**Write the ordered pair.**Remember that an ordered pair is written in the form . For the x-intercept, the value of will be the value you calculated previously, and the value will be 0, since always equals 0 at the x-intercept.^{[8]}- For example, for the line , the x-intercept is at the point .

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Method 3

Method 3 of 3:

### Using the Quadratic Formula

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1

**Determine that the equation of the line is a quadratic equation.**A quadratic equation is an equation that takes the form .^{[9]}A quadratic equation has two solutions, which means a line written in this form is a parabola and will have two x-intercepts.^{[10]}- For example, the equation is a quadratic equation, so this line will have two x-intercepts.

2

**Set up the quadratic formula.**The formula is , where equals the coefficient of the second-degree term (), equals the coefficient of the first-degree term (), and equals the constant.^{[11]}3

**Plug all of the values into the quadratic formula.**Make sure you substitute the correct values for each variable from the equation of the line.^{[12]}- For example, if the equation of your line is , your quadratic formula will look like this: .

4

**Simplify the equation.**To do this, first complete all of the multiplication. Make sure you pay close attention to all positive and negative signs.- For example:

- For example:
5

**Calculate the exponent.**Square the term. Then, add this number to the other number under the square root sign.^{[13]}- For example:

- For example:
6

**Solve for the addition formula.**Since the quadratic formula has a , you will solve once by adding, and once by subtracting. Solving by adding will give you your first value.^{[14]}- For example:

- For example:
7

**Solve for the subtraction formula.**This will give you the second value for . First calculate the square root, then find the difference in the numerator. Finally, divide by 2.^{[15]}- For example:

- For example:
8

**Find the ordered pairs for the x-intercept.**Remember that an ordered pair gives the x-coordinate first, then the y-coordinate . The values will be the values you calculated using the quadratic formula. The value will be 0, since at the x-intercept, always equals 0.^{[16]}- For example, for the line , the x-intercepts are at points and .

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## Expert Q&A

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Question

What is the x intercept?

David Jia

Math TutorDavid Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

The x intercept is wherever the line or the graph crosses the horizontal x axis.

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Question

How do you find the x intercept with a line equation?

See Also11.4: Graphing with InterceptsDavid Jia

Math TutorDavid Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

If you just have a simple equation like y=mx+b, you would find the x-intercept by substituting 0 for y and solving for x. If it's a quadratic equation, you'd solve by either factoring or using the quadratic equation.

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Question

What if the square root isnt perfect?

Donagan

Top Answerer

If you mean the square root is not a whole number, that's OK. It just means that the x-intercept will occur somewhere between two integers on the x-axis.

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## Tips

If you are working with the equation , you need to know the slope of the line and the y intercept. In the equation, m = the slope of the line and b = the y-intercept. Set y to equal zero, and solve for x. This will give you your x-intercept.

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## References

- ↑ http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/equations/x-y-intercepts/x-intercept-definition
- ↑ David Jia. Academic Tutor. Expert Interview. 14 January 2021.
- ↑ https://www.mathsisfun.com/definitions/ordered-pair.html
- ↑ http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/equations/x-y-intercepts/x-intercept-definition
- ↑ http://courses.wccnet.edu/~palay/precalc/22mt01.htm
- ↑ David Jia. Academic Tutor. Expert Interview. 14 January 2021.
- ↑ David Jia. Academic Tutor. Expert Interview. 14 January 2021.
- ↑ http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/equations/x-y-intercepts/x-intercept-definition
- ↑ http://mathworld.wolfram.com/QuadraticEquation.html

More References (7)

- ↑ http://www.csun.edu/~ayk38384/notes/mod11/Parabolas.html
- ↑ https://youtu.be/paaIu8KwCTg?t=114
- ↑ https://youtu.be/paaIu8KwCTg?t=180
- ↑ https://youtu.be/paaIu8KwCTg?t=241
- ↑ https://www.purplemath.com/modules/quadform.htm
- ↑ https://www.purplemath.com/modules/quadform.htm
- ↑ https://www.purplemath.com/modules/quadform.htm

## About This Article

Co-authored by:

David Jia

Math Tutor

This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 367,760 times.

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Co-authors: 14

Updated: June 12, 2023

Views:367,760

Categories: Algebra | Graphs

Article SummaryX

To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x. You can also use the graph of the line to find the x intercept. Just look on the graph for the point where the line crosses the x-axis, which is the horizontal axis. That point is the x intercept. To learn more, like how to find the x-intercept in a quadratic equation, keep reading the article!

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