Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define the gradient of a line.
• Calculate the gradient of a line given two points.
• Write the equation of a line using its gradient.
• Solve problems involving gradients and equations of lines.

Lesson summary

This lesson introduces the concepts of gradient (steepness) and the equation of a straight line. We see straight lines all around us in Ghana – the slope of the Aburi mountain road, the roof of a new building in our community, or even how the price of kenkey increases steadily over time. By understanding gradient, we can describe this steepness with a single number. We will then learn how to use this number to create a powerful mathematical sentence, called an equation, that describes the entire line. This skill connects geometry (drawing lines) with algebra (writing equations) and is a foundation for many future topics in mathematics and science.

Lesson notes

Part 1: The Gradient of a Line (Steepness)

The gradient of a line tells us two things: how steep it is, and in which direction it is sloping. In simple terms, it's the "rise" over the "run". Rise: The vertical change between two points on the line (how much you go up or down). Run: The horizontal change between the same two points (how much you go across).

We use the letter m to represent the gradient.

Formula for Gradient: If we have two points on a line, Point 1 `(x₁, y₁)` and Point 2 `(x₂, y₂)`, we can calculate the gradient using the formula: