📈 Gradient Gurus: Nail the Slope of Any Line!

The **gradient** (or slope) tells us how steep a straight line is. Mastering it is crucial for O Level exams because it links algebra, graphs, and real-world rates of change.

What Does Gradient Mean?

On a coordinate grid, the **gradient**

m

of a line is the ratio of the change in

y

to the change in

x

m = \frac{\text{vertical change}}{\text{horizontal change}} = \frac{y_2 - y_1}{x_2 - x_1}.

A **positive** gradient rises left → right, a **negative** one falls.

Choose two clear points on the line (grid intersections are safest).
Count the "rise" (up/down) and the "run" (right/left) between them.

Worked Example: Steep or Sleep?

Problem: The line shown passes through the grid points A(2, 1) and B(8, 5). Find its gradient.

Step 1: Pick the two points: $(2,1)$ and $(8,5)$ (clearly visible on the grid).
Step 2: Compute:
$m = \frac{5-1}{8-2} = \frac{4}{6} = \frac{2}{3}.$
The gradient is $\tfrac{2}{3}$ .

Practice sketching lines and calculating their gradients—exam questions love this! The more grids you tackle, the faster you’ll spot the rise-over-run and boost your graph confidence.