# 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.
• 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
``````

Copyright © 2017-2020 aidswidjaja and other contributors. CC BY-SA 4.0 Australia unless otherwise stated.