# Year 10+ Coordinate Geometry

### Chapters

### Using the Equation to Find the Intercepts

# Using the Equation to Find the Intercepts

## What are Intercepts?

`Intercepts`

are places where the graph of a function cuts the axes. As there are two axes in the \(xy\)-plane, there are two different types of intercepts:

- \(x\)-intercepts occur when the graph crosses the \(x\)-axis.
- \(y\)-intercepts occur when the graph crosses the \(y\)-axis.

## Finding the Intercepts

The **\(x\)-intercepts** lie on the **\(x\)-axis**, so their coordinates have the form \((x,0)\).

The **\(y\)-intercepts** lie on the **\(y\)-axis**, so their coordinates have the form \((0,y)\).

## Examples

### Example 1

Find the intercepts of the function \(y= x^2 - 1\).

**Solution:**

The \(x\)-intercepts occur when y = 0:

The \(y\)-intercepts occur when x = 0:

The graph looks like:

### Example 2

Find the intercepts of the function \(y= x^3 + 1\).

**Solution:**

The \(x\)-intercepts occur when y = 0:

The \(y\)-intercept occurs when x = 0:

The graph looks like:

### Example 3

Find the intercepts of the function \( x^2 + 6x + y^2 - 4y = 0 \).

**Solution:**

The \(x\)-intercepts occur when y = 0:

The \(y\)-intercepts occur when x = 0:

The graph looks like:

### Description

A **coordinate geometry** is a branch of **geometry** where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as **coordinates**. In this tutorial series, you will learn about vast range of topics such as Cartesian Coordinates, Midpoint of a Line Segment etc

### Audience

year 10 or higher, several chapters suitable for Year 8+ students.

### Learning Objectives

Explore topics related to Coordinates Geometry

Author: Subject Coach

Added on: 27th Sep 2018

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