x-intercept facts for kids

Imagine you're drawing a picture on a special kind of paper called a graph. This paper has two main lines: one goes across (the x-axis) and one goes up and down (the y-axis). When you draw a line on this graph, it might cross these main lines. The spot where your line crosses the x-axis is called the x-intercept.

What is an X-Intercept?

The x-intercept is a very important point on a graph. It's the exact spot where a line or a function's curve meets or crosses the horizontal line, which is the x-axis. At this point, the line has no height up or down from the x-axis. This means the y-value at the x-intercept is always zero.

For example, if a line crosses the x-axis at the number 3, its x-intercept is 3. We can also write this as a coordinate point: (3, 0). The first number is the x-value, and the second number is the y-value.

Finding the X-Intercept

Finding the x-intercept is like finding where a path crosses a main road. You can find it in a few ways:

• From a graph: Look at the graph and see where the line touches the x-axis. Read the number on the x-axis at that point.
• From an equation: If you have the equation of a line, like y = 2x - 6, you know that at the x-intercept, y is always 0. So, you can set y to 0 and solve for x.
  • Example:
    • Start with the equation: y = 2x - 6
    • Set y to 0: 0 = 2x - 6
    • Add 6 to both sides: 6 = 2x
    • Divide by 2: x = 3

So, the x-intercept is 3, or the point (3, 0).

Why are X-Intercepts Important?

X-intercepts are useful in many areas of mathematics and science. They can show us:

• Starting points: In some real-world problems, the x-intercept can represent a starting condition. For example, when something begins or ends.
• Solutions: For many equations, the x-intercepts are the "solutions" or "roots" of the equation. This means they are the values of x that make the equation true when y is zero.
• Break-even points: In business, an x-intercept might show the point where costs equal income, meaning there's no profit or loss.

Understanding x-intercepts helps us to better understand graphs and the information they show.

Related pages

• y-intercept
• Algebra

See also

In Spanish: Raíz de una función para niños