The key idea of equations and expressions at level 4 is that linear relationships between variables can be represented by a linear equation.

- a linear equation can involve number all four number operations (not including exponents)
- a linear equation can be solved in order to find an unknown variable in a particular situation

Linear equations take the form:*y* = *mx* + *c*.

At level 4 m is restricted to whole numbers (i.e. numbers without decimal points) and c is restricted to integers (i.e. can be either positive or negative whole numbers). When linear equations are represented on a graph, they form a straight line with the value of “*m*” corresponding to the slope and “*c*” representing the point where the line crosses the *y* axis.

Simple linear equations describe the relationship between two related variables, *x* and *y*. Any value of *x* has a corresponding value of* y*, and the linear relationship uniquely links the values of these two sets of variables. As the value of* x *varies, so does the value of *y*. Because the values of *x* and *y* are uniquely linked, a linear equation can be solved in order to find an unknown variable in a particular situation.

When working with equations that balance, such as linear equations, both sides of the equals sign need to be preserved for the equation to remain correct. For example, when the same number is subtracted from each side the equation remains accurate. For example 3p – 6 = 18 so 3p = 24 (adding six to both sides) so p = 8 (dividing both sides by three).

This key idea develops from the key idea of equations and expressions at level 3 that equations show relationships of equality between parts on either side of the equal sign.

This key idea links to the key idea of patterns and relationships at level 4.

This key idea is extended to the key idea of equations and expressions at level 5 that some types of relationships between variables can be represented by a quadratic equation.