# Year 8 Maths Chapter 7 - Linear Relationships 1

*You will want to refer to Year 9 Maths Chapter 4 for more advanced knowledge of linear relationships. This section is more advanced. For quadratics take a look at Year 9 Maths Chapter 8 and Year 9 Maths Chapter 10*

Basic terms and information:

- A
**number plane**(or Cartesian plane) includes a y-axis and an x-axis, intersecting at right angles, forming four quadrants. - Anti-clockwise from top-right: Quadrant 1 - Quadrant 4.
- Point on a number plane has
**coordinates**:`(x, y)`

, where x is number of horizontal units from origin (x-coordinate) and vice versa (vertical units, y-coordinate). - The point
`(0, 0)`

is known as the**origin**. - A
**rule**or a**formula**is an equation connecting two or more variables. - A straight line forms a
**linear**rule. - Linear rules are often written with y as the subject. For example,
`y = 3x - 2`

You can use a **table of values** to find a rule. The rule must be true for every pair of coordinates, substituted into a table or graph.

For example:

```
y = ☐x + ☐
```

To find a rule, use the formula below.

```
y = mx + b
```

where m is the gradient and b is the y-intercept. This is known as **gradient-intercept form**.

- The
**gradient**is rise over run. - On a graph, it is the steepness of a line, measured by a specific height measurement, over a specific length measurement.
- For example, for a gradient to be 2, on a graph the line would be increasing in height, and for every 5 units on the x axis, there would be a growth of 10 units.
- In a table of values, it is the difference in the y-axis between every consecutive number on the x-axis
- The
**y-intercept**is the constant value when`x = 0`

. - The
**x-intercept**is the constant value where`y = 0`

.

A linear equation has a solution, where a pair of values, representing x-coordinates and y-coordinates, solve an equation when substituted into their relative pronumerals.

Where there are two straight lines crossing over, there is a point of intersection (the point where the lines cross). In this case, the point of intersection is the pair of values that satisfies both rules.

Non-linear relationships are graphs or rules that are not linear (form a curve, such as a parabola).

An example of a non-linear curve:

```
y = x^2
```