Math & Geometry Tool

Line Intersection Calculator

Find the exact point where two straight lines meet. Enter the slope and y-intercept for each line and get your intersection point instantly.

Calculate Line Intersection

Enter values for both linear equations

Line 1 y = m₁x + b₁

Slope (m₁)

Enter the slope of Line 1.

Y-Intercept (b₁)

Enter where Line 1 crosses the y-axis.

Line 2 y = m₂x + b₂

Slope (m₂)

Enter the slope of Line 2.

Y-Intercept (b₂)

Enter where Line 2 crosses the y-axis.

Clear Calculator

Intersection Formula

How the result is calculated

x = (b₂ − b₁) ÷ (m₁ − m₂)
y = m₁x + b₁

For two lines written as y = m₁x + b₁ and y = m₂x + b₂, the calculator first finds the x-coordinate and then substitutes it into either line to determine y.

Tip: If both lines have the same slope, they are either parallel or exactly the same line.

What Is a Line Intersection Calculator?

A Line Intersection Calculator is a mathematical tool that determines the exact point where two straight lines cross each other. The result is normally written as an ordered pair in the form (x, y).

This calculator works with linear equations in slope-intercept form, written as y = mx + b. Here, m represents the slope of the line and b represents its y-intercept.

When two lines have different slopes, they will normally meet at one unique point. The calculator uses the two equations to determine that point without requiring you to solve the equations manually.

How to Use the Line Intersection Calculator

Enter the slope and y-intercept for each line. The calculator will compare the equations and determine whether the lines intersect, are parallel, or are identical.

Enter Line 1

Enter the slope and y-intercept of the first line in the corresponding fields.

Enter Line 2

Add the slope and y-intercept of the second line using the same format.

Get the Result

Click the calculate button to instantly see the intersection coordinates.

Example of Finding a Line Intersection

Suppose the first line is y = 2x + 3 and the second line is y = -x + 6.

The slopes are 2 and -1, while the y-intercepts are 3 and 6. Using the intersection formula:

x = (6 − 3) ÷ (2 − (-1))
x = 3 ÷ 3
x = 1

y = 2(1) + 3
y = 5

Therefore, the two lines intersect at (1, 5).

Frequently Asked Questions

What is the intersection of two lines?

The intersection is the point where two lines cross. It is usually represented by an ordered pair such as (x, y).

What formula is used to find line intersection?

For y = m₁x + b₁ and y = m₂x + b₂, the x-coordinate can be found using x = (b₂ − b₁) / (m₁ − m₂). The x-value is then substituted into either equation to find y.

What happens if two lines have the same slope?

If two lines have the same slope but different y-intercepts, they are parallel and never intersect. If both slope and intercept are the same, the lines are identical and have infinitely many common points.

Can this calculator find decimal intersections?

Yes. The calculator accepts decimal values for slopes and y-intercepts and displays the resulting coordinates with up to six decimal places.

What form of equation does this calculator use?

It uses the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

Is the Line Intersection Calculator free to use?

Yes. You can use the calculator to find line intersections quickly without performing the calculations manually.