How to Find the X Intercept

Co-authored by David Jia

Last Updated: October 11, 2024 Fact Checked

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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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]
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Research source} It is important to look at the x-axis when locating the x-intercept.
The x-intercept is this point. ^{[2]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 14 January 2021.} 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
Write the ordered pair for the x-intercept. An ordered pair is written in the form $(x,y)$ and gives you the coordinates for the point on the line. ^{[3]
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Research source} 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]
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Research source}
- For example, if a line crosses the x-axis at point 4, the ordered pair for the x-intercept is $(4,0)$ .

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 $Ax+By=C$ . ^{[5]
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Research source} In this form, $A$ , $B$ , and $C$ are integers, and $x$ and $y$ are the coordinates of a point on the line.
- For example, you might be given the equation $2x+3y=6$ .
2
Plug in 0 for $y$ . The x-intercept is the point on the line where the line crosses the x-axis. At this point, the value for $y$ will be 0. So, in order to find the x-intercept, you need to set the $y$ to 0 and solve for $x$ . ^{[6]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 14 January 2021.}
- For example, if you substitute 0 for $y$ , your equation will look like this: $2x+3(0)=6$ , which simplifies to $2x=6$ .
3
Solve for $x$ . 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 $x$ when $y=0$ , which is the x-intercept. ^{[7]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 14 January 2021.}
- For example:
  $2x=6$
  ${\frac {2x}{2}}={\frac {6}{2}}$
  $x=3$
4
Write the ordered pair. Remember that an ordered pair is written in the form $(x,y)$ . For the x-intercept, the value of $x$ will be the value you calculated previously, and the $y$ value will be 0, since $y$ always equals 0 at the x-intercept. ^{[8]
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Research source}
- For example, for the line $2x+3y=6$ , the x-intercept is at the point $(3,0)$ .

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 $ax^{{2}}+bx+c=0$ . ^{[9]
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Research source} A quadratic equation has two solutions, which means a line written in this form is a parabola and will have two x-intercepts. ^{[10]
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Research source}
- For example, the equation $x^{{2}}+3x-10=0$ is a quadratic equation, so this line will have two x-intercepts.
The formula is $x={\frac {-b\pm {\sqrt {b^{{2}}-4ac}}}{2a}}$ , where $a$ equals the coefficient of the second-degree term ( $x^{{2}}$ ), $b$ equals the coefficient of the first-degree term ( $x$ ), and $c$ equals the constant. ^{[11]
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Research source}
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]
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Research source}
- For example, if the equation of your line is $x^{{2}}+3x-10=0$ , your quadratic formula will look like this: $x={\frac {-3\pm {\sqrt {3^{{2}}-4(1)(-10)}}}{2(1)}}$ .
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. ^{[13]
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Research source}
- For example:
  $x={\frac {-3\pm {\sqrt {3^{{2}}-4(-10)}}}{2(1)}}$
  $x={\frac {-3\pm {\sqrt {3^{{2}}+40}}}{2}}$
5
Calculate the exponent. Square the $b$ term. Then, add this number to the other number under the square root sign. ^{[14]
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Research source}
- For example:
  $x={\frac {-3\pm {\sqrt {3^{{2}}+40}}}{2}}$
  $x={\frac {-3\pm {\sqrt {9+40}}}{2}}$
  $x={\frac {-3\pm {\sqrt {49}}}{2}}$
6
Solve for the addition formula. Since the quadratic formula has a $\pm$ , you will solve once by adding, and once by subtracting. Solving by adding will give you your first $x$ value. ^{[15]
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Research source}
- For example:
  $x={\frac {-3+{\sqrt {49}}}{2}}$
  $x={\frac {-3+7}{2}}$
  $x={\frac {4}{2}}$
  $x=2$
7
Solve for the subtraction formula. This will give you the second value for $x$ . First calculate the square root, then find the difference in the numerator. Finally, divide by 2. ^{[16]
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Research source}
- For example:
  $x={\frac {-3-{\sqrt {49}}}{2}}$
  $x={\frac {-3-7}{2}}$
  $x={\frac {-10}{2}}$
  $x=-5$
8
Find the ordered pairs for the x-intercept. Remember that an ordered pair gives the x-coordinate first, then the y-coordinate $(x,y)$ . The $x$ values will be the values you calculated using the quadratic formula. The $y$ value will be 0, since at the x-intercept, $y$ always equals 0. ^{[17]
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Research source}
- For example, for the line $x^{{2}}+3x-10=0$ , the x-intercepts are at points $(2,0)$ and $(-5,0)$ .

Expert Q&A

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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

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Expert Answer

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

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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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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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If you are working with the equation $y=mx+b$ , 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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How to Find the X Intercept

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Using a Graph of a Line

Using the Equation of the Line

Using the Quadratic Formula

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