2. Algebra & Graphs

Linear Graphs

As you prepare for your Maths exam, understanding linear graphs is essential. In this comprehensive guide, we'll explore the key concepts, provide examples, and share exam tips to help you succeed in any questions related to linear graphs. Let's dive into the world of linear graphs and make sure you're fully prepared for your Maths exam!

What is a Linear Graph?

A linear graph is a straight line that represents the relationship between two variables. Linear graphs are expressed in the form $y = m x + c$ , where ' $m$ ' is the gradient (slope) of the line, and ' $c$ ' is the y-intercept (the point at which the line crosses the y-axis).

How do I find the gradient?

The gradient, or slope, of a linear graph indicates the steepness of the line.

To calculate the gradient, use the following formula:

$m = \frac{change in y}{change in x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

What type of linear graphs questions could I be asked?

There are lots of different questions you may be asked, here are some common examples. For lots more check out our Linear Graphs Topic Questions

Example 1: Finding the gradient and y-intercept

Question: Identify the gradient and y-intercept of the following equation: $y = 3 x - 2$ .

Solution: Compare the given equation $y = 3 x - 2$ with $y = m x + c$ . The coefficient (number in front) of $x$ is the gradient so $m = 3$ . The constant term $c$ is the y-intercept so $c = - 2$ .

Example 2: Drawing a Linear Graph

Question: Draw the graph of the equation $y = - 2 x + 4$ .

Solution:

gradient--2-y-intercept-4

Method 1: You may want to draw a table of values to find coordinate points to plot.

$x$	$0$	$1$	$2$	$3$	$4$
$y = - 2 x + 4$	$4$	$2$	$0$	$- 2$	$- 4$

Method 2: First identify the gradient and y-intercept.

The gradient is $- 2$ , and the y-intercept is $4$ .

Plot the y-intercept as a coordinate point $(0, 4)$ on the y-axis.

Since the gradient is $- 2$ , move two units down and one unit to the right to find the next point $(1, 2)$ .

Continue this process to plot more points, and then draw a straight line through the points.

Linear Graph Exam Tips

Memorise the Equation of a Line

Remember the equation of a line in the form $y = m x + c$ . This will help you identify the gradient and y-intercept quickly and accurately.

Practice Drawing Linear Graphs

Familiarise yourself with drawing linear graphs using different gradients and y-intercepts. This will help you visualise the relationships between variables and become more confident in answering questions about linear graphs.

Understand How to Calculate the Gradient

Be comfortable with the gradient formula and how to use it to find the slope of a line. This skill is essential for solving problems related to linear graphs.

Linear graphs: Examiner's Tips

Mastering linear graphs is an essential skill for achieving top grades in your Maths exam. By understanding the key concepts, practising drawing graphs, and becoming comfortable with the gradient and y-intercept, you'll be well-prepared for any questions related to linear graphs.

CIE IGCSE Maths: Extended

Revision Notes