Y-Intercept Calculator

Find the y-intercept of a linear equation using the slope and x-intercept. Get the answer, equation, and calculation steps instantly.

Calculate Y-Intercept

Linear Equation y = mx + b

Slope

Enter the slope of the line.

X-Intercept

Enter the x-coordinate of the x-intercept.

Examples:

Y-Intercept

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Calculation Steps

What Is a Y-Intercept?

The y-intercept is the point where a line crosses the y-axis. At the y-axis, the x-coordinate is always zero.

x = 0

Therefore, a y-intercept is normally written as (0, b), where b is the y-intercept value.

How to Use This Calculator

You can calculate the y-intercept when you know the slope and the x-intercept.

Enter the slope of the line.
Enter the x-intercept.
Click the Calculate button.
View the y-intercept and coordinate.

Y-Intercept Formula

A linear equation can be written in slope-intercept form as:

y = mx + b

At the x-intercept, y equals zero. If the x-intercept is represented by x₀, then:

0 = mx₀ + b

Solving for b gives:

b = −mx₀

The y-intercept point is therefore:

(0, −mx₀)

Example Calculation

Suppose the slope is 2 and the x-intercept is −3.

b = −mx₀

b = −(2)(−3) = 6

The y-intercept is therefore:

(0, 6)

Y-Intercept vs X-Intercept

The two intercepts identify where a line crosses the coordinate axes.

Y-Intercept = (0, y)

X-Intercept = (x, 0)

Why Is the Y-Intercept Important?

The y-intercept is useful when graphing linear equations and interpreting mathematical models. It identifies the value of y when x is zero.

Graphing straight lines.
Understanding slope-intercept form.
Finding an initial or starting value.
Analyzing linear relationships.

Frequently Asked Questions

What is a y-intercept?

A y-intercept is the point where a line crosses the y-axis. Its x-coordinate is always zero.

What is the formula for a y-intercept?

If the slope is m and the x-intercept is x₀, the y-intercept value is b = −mx₀.

What is the y-intercept of a line with slope 2 and x-intercept -3?

Using b = −mx₀, we get b = −(2)(−3) = 6. The y-intercept is therefore (0, 6).

Can a y-intercept be negative?

Yes. A line can cross the y-axis below the origin, producing a negative y-intercept.

Where is the y-intercept located?

The y-intercept is located on the y-axis, where x equals zero.

What does b represent in y = mx + b?

The letter b represents the y-intercept of the line. The corresponding point is (0, b).