How to Find the y-Intercept of a Line?

Finding the y-intercept of a line is as simple as setting \(\color{blue}{x = 0}\) in the equation and solving for \(\color{blue}{y}\). The y-intercept is the point where a line crosses the vertical axis, and it appears directly in the slope-intercept equation \(\color{blue}{y = \text{ mx } + b}\) as the constant \(\color{blue}{b}\). This guide explains every method with worked examples, two video lessons, and practice problems.

What Is the y-Intercept?

The y-intercept is the point where a line meets the y-axis. Because every point on the y-axis has an x-coordinate of zero, the y-intercept always has the form \(\color{blue}{(0, b)}\). In slope-intercept form \(\color{blue}{y = \text{ mx } + b}\), the constant \(\color{blue}{b}\) is the y-intercept value.

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How to Find the y-Intercept

From slope-intercept form

In \(\color{blue}{y = \text{ mx } + b}\), the y-intercept is simply \(\color{blue}{b}\) — no calculation needed.

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

By substituting \(\color{blue}{x = 0}\)

Plug \(\color{blue}{x = 0}\) into any form of the equation and solve for \(\color{blue}{y}\).

Example: \(\color{blue}{4x – 2y = 8}\) ⇒ \(\color{blue}{4(0) – 2y = 8 \Rightarrow -2y = 8 \Rightarrow y = -4}\). Y-intercept: \(\color{blue}{(0, -4)}\).

From a graph

Read the y-coordinate of the point where the line crosses the y-axis. It always has x-coordinate 0.

Step-by-Step Summary

1. Write or identify the equation of the line.
2. Substitute \(\color{blue}{x = 0}\) into the equation.
3. Solve the resulting equation for \(\color{blue}{y}\).
4. Write the y-intercept as \(\color{blue}{(0, y)}\).

Watch: Finding the y-Intercept (Video Lesson)

Khan Academy shows how to find the y-intercept when you are given a slope and a point on the line:

Finding the y-Intercept – Worked Examples

Example 1: Find the y-intercept of \(\color{blue}{y = 2x + 5}\).

The equation is already in slope-intercept form. The y-intercept is \(\color{blue}{b = 5}\).
Y-intercept: \(\color{blue}{(0, 5)}\)

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

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

Example 3: Find the y-intercept of \(\color{blue}{y = -x + 7}\).

Set \(\color{blue}{x = 0}\): \(\color{blue}{y = -(0) + 7 = 7}\)
Y-intercept: \(\color{blue}{(0, 7)}\)

Example 4: Find the y-intercept of \(\color{blue}{3x + 5y = 15}\).

Set \(\color{blue}{x = 0}\): \(\color{blue}{5y = 15 \Rightarrow y = 3}\)
Y-intercept: \(\color{blue}{(0, 3)}\)

More Practice: Slope and y-Intercept from Slope-Intercept Form (Video)

Math with Mr. J demonstrates how to read both the slope and the y-intercept directly from the equation:

Exercises for Finding the y-Intercept

Find the y-intercept of each line.

1. \(\color{blue}{y = 3x – 6}\)
2. \(\color{blue}{y = -(\frac{1}{2})x + 4}\)
3. \(\color{blue}{2x + y = 9}\)
4. \(\color{blue}{5x – 3y = -12}\)
5. \(\color{blue}{y = 7}\)

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Answers

1. \(\color{blue}{(0, -6)}\)
2. \(\color{blue}{(0, 4)}\)
3. \(\color{blue}{(0, 9)}\)
4. \(\color{blue}{(0, 4)}\)
5. \(\color{blue}{(0, 7)}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Finding the y-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 does the y-intercept tell you about a real-world situation?

The y-intercept represents the starting value of a quantity when the input (\(\color{blue}{x}\)) is zero. For example, if \(\color{blue}{y}\) represents total cost, \(\color{blue}{b}\) might be a one-time fixed fee paid before any units are purchased.

Can a line have two y-intercepts?

No. A non-horizontal function can cross the y-axis at most once. Every non-vertical line has exactly one y-intercept.

What is the y-intercept of a vertical line?

A vertical line of the form \(\color{blue}{x = c}\) crosses the y-axis only when \(\color{blue}{c = 0}\), giving a y-intercept at every point of the y-axis. If \(\color{blue}{c \ne 0}\), the vertical line has no y-intercept.

Related Topics

• Finding the x-Intercept
• Finding Slope
• Writing Linear Equations
• Write an Equation from a Graph
• Point-Slope Form of Equations