Knowing how to calculate the gradient of a graph is a fundamental skill that students will learn and develop as they progress through their first years of secondary education and, ultimately, start to prepare for GCSE maths exams.

In this article, we’ll look at what the gradient of a line is, how to calculate it, and some examples of how knowledge of this topic might be tested in exam questions.

What is the gradient of a line?

The gradient of a line is a measure of its slope. The steeper a straight line appears on a graph, the greater its gradient.

Working from left to right, a line with a positive gradient will slope upwards, while a line with a negative gradient will always have a downward slope.

Here are some other useful facts to bear in mind when working with gradients of straight lines:

• Parallel lines always have the same gradient
• Perpendicular lines on a graph slope in opposite directions, meaning one has a positive gradient and the other a negative gradient
• The product of the gradients of perpendicular lines will always be -1

How to calculate the gradient of a line graph

To find the gradient of a straight line graph:

• Take two points on the line (any points will work, but finding points that align with whole numbers on the x and y axes can make the calculation easier)
• Calculate the differences in the x and y coordinates between the points
• Divide the difference in the y coordinates by the difference in the x coordinates

If, for example, you have a line with two points at the coordinates (2, 0) and (8, 3), the differences between the x and y coordinates are 6 and 3, respectively. The gradient, in this case, would be calculated by dividing 3 by 6, to give 0.5. As the value of y increases with x, we can be sure that the gradient is positive.

Another method is to draw a right-angled triangle between your two chosen points, with the straight line graph forming the longest side. Divide the height of the triangle by the width to find the gradient of the line.

Gradient of a line GCSE questions

When the time comes to start revising this topic ahead of GCSE exams, it’s useful to think about the sorts of questions that are likely to come up in examination papers.

This can help with checking and strengthening your understanding of concepts such as positive and negative gradients and comparing equations of perpendicular lines. For example, you might be asked to:

• Find the gradient of a line presented on a graph
• Plot a straight line on a graph from given coordinates and find the gradient of the line
• Find the gradient of a line presented as a function
• Draw the graph of the given function
• Find a function that would produce a line perpendicular to the one already given
• Find the equation of a line plotted on a graph

Having access to a calculator and developing the skills to use it confidently is hugely beneficial for GCSE maths students, particularly when it comes to performing tricky calculations (those involving complex graph coordinates, for example) and checking work.

Take a look at our range of exam-approved GCSE calculators.