### Solving Linear Relationships – what are they?

A **linear relationship or ‘function’ **makes a straight line when graphed onto a number plane. These equations have a dependent and independent variable. Solving linear relationship requires you to graph these functions. To do so, you need to construct a table that contains the independent variable on the top row, followed by the dependent variable being solved by substituting into the equation. Plot the answers on the graph and your answer will form a linear relationship, in other words, will be a straight line.

The following videos will show you how to construct both the table and the graph in order to solve linear relationships in HSC Standard Math.

### Independent and Dependent Variables

The video below explains the difference between independent and dependent variables in HSC Standard Math.

### How to solve the linear relationship using a table, and plot on a graph.

The video below explains how you will be able to input your answers into a table and plot onto a graph.

### How to find the gradient and y-intercept and the equation of a straight line.

The following video explains how to find the gradient of the straight line, the y-intercept, and further the equation of the line in the form y=mx+c.

### Using the Gradient-Intercept formula – y=mx+c

Using the information you have learned from the video above, you will be able to use the gradient-intercept formula. The following video shows you how to use the formula to sketch a graph.

### Parallel Lines

If the value of the gradient (m) is the same for two linear functions, the lines are parallel. The following video will explain this concept and go through an example.