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