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:

In this picture, you can see the line and its intercepts. The red dot shows where the line crosses the x-axis (the X-intercept), and the green dot shows where it crosses the y-axis (the Y-intercept). It's like the line is playing connect-the-dots with these special points!