How to Find the x-Intercept of a Line?

Finding the x-intercept of a line is one of the quickest skills in Algebra 1: simply set \(\color{blue}{y = 0}\) in the equation and solve for \(\color{blue}{x}\). The x-intercept is the point where the line crosses the horizontal axis, and it tells you the value of \(\color{blue}{x}\) when there is no vertical component. Mastering this technique helps with graphing, writing equations, and solving real-world problems.

What Is the x-Intercept?

The x-intercept is the point where a line meets the x-axis. At that point, the y-coordinate is always zero, so the x-intercept is the ordered pair \(\color{blue}{(x, 0)}\). To find it, substitute \(\color{blue}{y = 0}\) into the line’s equation and solve.

Algebra I for Beginners 2026 The Ultimate Step by Step Guide to Acing Algebra I

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

How to Find the x-Intercept

From slope-intercept form

Set \(\color{blue}{y = 0}\) in \(\color{blue}{y = \text{ mx } + b}\) and solve: \(\color{blue}{0 = \text{ mx } + b \Rightarrow x = -\frac{b}{m}}\).

Example: \(\color{blue}{y = 3x + 6}\) ⇒ \(\color{blue}{0 = 3x + 6 \Rightarrow 3x = -6 \Rightarrow x = -2}\). X-intercept: \(\color{blue}{(-2, 0)}\).

From standard form

Set \(\color{blue}{y = 0}\) in \(\color{blue}{\text{ Ax } + \text{ By } = C}\): the \(\color{blue}{\text{ By }}\) term drops out, leaving \(\color{blue}{\text{ Ax } = C \Rightarrow x = \frac{C}{A}}\).

Example: \(\color{blue}{5x + 2y = 10}\) ⇒ \(\color{blue}{5x = 10 \Rightarrow x = 2}\). X-intercept: \(\color{blue}{(2, 0)}\).

From a graph

Read the x-coordinate of the point where the line crosses the x-axis. It is always at height \(\color{blue}{y = 0}\).

Step-by-Step Summary

1. Write the equation of the line.
2. Substitute \(\color{blue}{y = 0}\).
3. Solve the resulting one-variable equation for \(\color{blue}{x}\).
4. Write the answer as an ordered pair \(\color{blue}{(x, 0)}\).

Watch: Finding the x-Intercept (Video Lesson)

This Khan Academy lesson walks through finding the x-intercept from an equation with clear explanations:

Finding the x-Intercept – Worked Examples

Example 1: Find the x-intercept of \(\color{blue}{y = 3x + 6}\).

Set \(\color{blue}{y = 0}\): \(\color{blue}{0 = 3x + 6 \Rightarrow -6 = 3x \Rightarrow x = -2}\)
X-intercept: \(\color{blue}{(-2, 0)}\)

Example 2: Find the x-intercept of \(\color{blue}{2x – 4y = 8}\).

Set \(\color{blue}{y = 0}\): \(\color{blue}{2x – 0 = 8 \Rightarrow x = 4}\)
X-intercept: \(\color{blue}{(4, 0)}\)

Example 3: Find the x-intercept of \(\color{blue}{y = -3x + 9}\).

Set \(\color{blue}{y = 0}\): \(\color{blue}{0 = -3x + 9 \Rightarrow 3x = 9 \Rightarrow x = 3}\)
X-intercept: \(\color{blue}{(3, 0)}\)

Example 4: Find the x-intercept of \(\color{blue}{5x + 2y = 10}\).

Set \(\color{blue}{y = 0}\): \(\color{blue}{5x + 0 = 10 \Rightarrow x = 2}\)
X-intercept: \(\color{blue}{(2, 0)}\)

More Practice: X and Y Intercepts (Video)

The Organic Chemistry Tutor covers both intercepts from equations in multiple forms, making this a great second resource:

Exercises for Finding the x-Intercept

Find the x-intercept of each line.

1. \(\color{blue}{y = 2x – 8}\)
2. \(\color{blue}{y = -x + 5}\)
3. \(\color{blue}{4x + 3y = 12}\)
4. \(\color{blue}{y = (\frac{1}{2})x + 3}\)
5. \(\color{blue}{6x – 2y = 18}\)

Algebra I Practice Workbook 2026 The Most Comprehensive Review of Algebra 1

Download

$29.99 Original price was: $29.99.$19.99Current price is: $19.99.

Answers

1. \(\color{blue}{(4, 0)}\)
2. \(\color{blue}{(5, 0)}\)
3. \(\color{blue}{(3, 0)}\)
4. \(\color{blue}{(-6, 0)}\)
5. \(\color{blue}{(3, 0)}\)

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Want More Practice?

We haven’t published a worksheet built specifically for Finding the x-Intercept just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Slope Intercept Form Worksheet
• Download Standard Form of a Linear Equation Worksheet
• Download Writing Linear Equations from Graphs and Tables Worksheet

Frequently Asked Questions

What is the x-intercept used for?

The x-intercept shows where a quantity reaches zero on the horizontal axis. In real-world problems it can represent a break-even point, a time when an amount runs out, or the starting position of an object.

Can a line have more than one x-intercept?

No. A non-vertical line can cross the x-axis at most once, so it has exactly one x-intercept (or none, if it is a horizontal line that does not touch the x-axis).

What is the x-intercept of a horizontal line?

A horizontal line of the form \(\color{blue}{y = c}\) only crosses the x-axis if \(\color{blue}{c = 0}\), in which case every point on the line is an x-intercept. If \(\color{blue}{c \ne 0}\), there is no x-intercept.

Related Topics

• Finding the y-Intercept
• Finding Slope
• Writing Linear Equations
• Write an Equation from a Graph
• Properties of the Horizontal Line