3 Ways to Find the X Intercept - wikiHow (2024)

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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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Co-authored byDavid 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. 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. 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).

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  3. 3

    Write the ordered pair for the x-intercept. An ordered pair is written in the form 3 Ways to Find the X Intercept - wikiHow (7) 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 3 Ways to Find the X Intercept - wikiHow (8).
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Method 2

Method 2 of 3:

Using the Equation of the Line

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  1. 1

    Determine that the equation of the line is in standard form. The standard form of a linear equation is 3 Ways to Find the X Intercept - wikiHow (11).[5] In this form, 3 Ways to Find the X Intercept - wikiHow (12), 3 Ways to Find the X Intercept - wikiHow (13), and 3 Ways to Find the X Intercept - wikiHow (14) are integers, and 3 Ways to Find the X Intercept - wikiHow (15) and 3 Ways to Find the X Intercept - wikiHow (16) are the coordinates of a point on the line.

    • For example, you might be given the equation 3 Ways to Find the X Intercept - wikiHow (17).
  2. 2

    Plug in 0 for 3 Ways to Find the X Intercept - wikiHow (19). The x-intercept is the point on the line where the line crosses the x-axis. At this point, the value for 3 Ways to Find the X Intercept - wikiHow (20) will be 0. So, in order to find the x-intercept, you need to set the 3 Ways to Find the X Intercept - wikiHow (21) to 0 and solve for 3 Ways to Find the X Intercept - wikiHow (22).[6]

    • For example, if you substitute 0 for 3 Ways to Find the X Intercept - wikiHow (23), your equation will look like this: 3 Ways to Find the X Intercept - wikiHow (24), which simplifies to 3 Ways to Find the X Intercept - wikiHow (25).
  3. 3

    Solve for 3 Ways to Find the X Intercept - wikiHow (27). 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 3 Ways to Find the X Intercept - wikiHow (28) when 3 Ways to Find the X Intercept - wikiHow (29), which is the x-intercept.[7]

    • For example:
      3 Ways to Find the X Intercept - wikiHow (30)
      3 Ways to Find the X Intercept - wikiHow (31)
      3 Ways to Find the X Intercept - wikiHow (32)
  4. 4

    Write the ordered pair. Remember that an ordered pair is written in the form 3 Ways to Find the X Intercept - wikiHow (34). For the x-intercept, the value of 3 Ways to Find the X Intercept - wikiHow (35) will be the value you calculated previously, and the 3 Ways to Find the X Intercept - wikiHow (36) value will be 0, since 3 Ways to Find the X Intercept - wikiHow (37) always equals 0 at the x-intercept.[8]

    • For example, for the line 3 Ways to Find the X Intercept - wikiHow (38), the x-intercept is at the point 3 Ways to Find the X Intercept - wikiHow (39).
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Method 3

Method 3 of 3:

Using the Quadratic Formula

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  1. 1

    Determine that the equation of the line is a quadratic equation. A quadratic equation is an equation that takes the form 3 Ways to Find the X Intercept - wikiHow (42).[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 3 Ways to Find the X Intercept - wikiHow (43) is a quadratic equation, so this line will have two x-intercepts.
  2. 2

    Set up the quadratic formula. The formula is 3 Ways to Find the X Intercept - wikiHow (45), where 3 Ways to Find the X Intercept - wikiHow (46) equals the coefficient of the second-degree term (3 Ways to Find the X Intercept - wikiHow (47)), 3 Ways to Find the X Intercept - wikiHow (48) equals the coefficient of the first-degree term (3 Ways to Find the X Intercept - wikiHow (49)), and 3 Ways to Find the X Intercept - wikiHow (50) equals the constant.[11]

  3. 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 3 Ways to Find the X Intercept - wikiHow (52), your quadratic formula will look like this: 3 Ways to Find the X Intercept - wikiHow (53).
  4. 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:
      3 Ways to Find the X Intercept - wikiHow (55)
      3 Ways to Find the X Intercept - wikiHow (56)
  5. 5

    Calculate the exponent. Square the 3 Ways to Find the X Intercept - wikiHow (58) term. Then, add this number to the other number under the square root sign.[13]

    • For example:
      3 Ways to Find the X Intercept - wikiHow (59)
      3 Ways to Find the X Intercept - wikiHow (60)
      3 Ways to Find the X Intercept - wikiHow (61)
  6. 6

    Solve for the addition formula. Since the quadratic formula has a 3 Ways to Find the X Intercept - wikiHow (63), you will solve once by adding, and once by subtracting. Solving by adding will give you your first 3 Ways to Find the X Intercept - wikiHow (64) value.[14]

    • For example:
      3 Ways to Find the X Intercept - wikiHow (65)
      3 Ways to Find the X Intercept - wikiHow (66)
      3 Ways to Find the X Intercept - wikiHow (67)
      3 Ways to Find the X Intercept - wikiHow (68)
  7. 7

    Solve for the subtraction formula. This will give you the second value for 3 Ways to Find the X Intercept - wikiHow (70). First calculate the square root, then find the difference in the numerator. Finally, divide by 2.[15]

    • For example:
      3 Ways to Find the X Intercept - wikiHow (71)
      3 Ways to Find the X Intercept - wikiHow (72)
      3 Ways to Find the X Intercept - wikiHow (73)
      3 Ways to Find the X Intercept - wikiHow (74)
  8. 8

    Find the ordered pairs for the x-intercept. Remember that an ordered pair gives the x-coordinate first, then the y-coordinate 3 Ways to Find the X Intercept - wikiHow (76). The 3 Ways to Find the X Intercept - wikiHow (77) values will be the values you calculated using the quadratic formula. The 3 Ways to Find the X Intercept - wikiHow (78) value will be 0, since at the x-intercept, 3 Ways to Find the X Intercept - wikiHow (79) always equals 0.[16]

    • For example, for the line 3 Ways to Find the X Intercept - wikiHow (80), the x-intercepts are at points 3 Ways to Find the X Intercept - wikiHow (81) and 3 Ways to Find the X Intercept - wikiHow (82).
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  • Question

    What is the x intercept?

    David Jia
    Math Tutor

    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.

    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?

    David Jia
    Math Tutor

    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.

    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?

    3 Ways to Find the X Intercept - wikiHow (87)

    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 3 Ways to Find the X Intercept - wikiHow (88), 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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      About This Article

      3 Ways to Find the X Intercept - wikiHow (104)

      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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