X and Y Intercepts Calculator

x +
y +
= 0

Enter the coefficients A, B, and C for the equation Ax + By + C = 0. See Example

x y

X and Y Intercepts Calculator

What are X and Y Intercepts?

X and Y intercepts are special points where a line crosses the x-axis and y-axis on a graph. Imagine a tightrope walker balancing on a rope. The places where the rope touches the ground are like the intercepts!

How to Calculate X and Y Intercepts

Finding X and Y intercepts is like solving a fun puzzle. We use the equation of the line to figure out where it meets each axis. It's a bit like finding out where your jump rope touches the ground when you swing it!

Formula

The main formula for a line is:

\[ Ax + By + C = 0 \]

Where:

  • \(A\), \(B\), and \(C\) are numbers that define the line
  • \(x\) and \(y\) are the coordinates of any point on the line

Calculation Steps

  1. For the X-intercept: Set \(y = 0\) and solve for \(x\)
  2. For the Y-intercept: Set \(x = 0\) and solve for \(y\)
  3. The X-intercept is the point \((x, 0)\)
  4. The Y-intercept is the point \((0, y)\)

Example and Visual Representation

Let's look at the line \(2x + 3y - 6 = 0\):

  • X-intercept: When \(y = 0\), \(2x - 6 = 0\), so \(x = 3\). The X-intercept is \((3, 0)\).
  • Y-intercept: When \(x = 0\), \(3y - 6 = 0\), so \(y = 2\). The Y-intercept is \((0, 2)\).

Here's what this line and its intercepts look like:

-8 -4 4 8 8 4 -4 -8 (3, 0) (0, 2) 2x + 3y - 6 = 0 X-intercept: y = 0 → 2x - 6 = 0 → x = 3 Y-intercept: x = 0 → 3y - 6 = 0 → y = 2