O Level MathematicsE3.3 Gradient of linear graphs (calculate using coordinates $m = (y_2 - y_1) / (x_2 - x_1)$).

📈 Mastering Gradients Made Easy!

Edudent Academy
29 Dec 25

Understanding how to calculate the gradient of a straight line is **vital** for success in O-Level Mathematics. It not only appears in coordinate geometry questions but also underpins concepts such as parallel and perpendicular lines, kinematics graphs, and even rate of change in higher studies.

Main Concept: What is Gradient?

The gradient (or slope) of a line measures its steepness. Using two coordinate points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we find the gradient with the formula
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
. A **positive** value means the line ascends from left to right, a **negative** value means it descends, and a gradient of **0** represents a horizontal line.

Worked Example: Line Through (2,3) & (6,11)

  • Problem: Find the gradient of the straight line joining the points (2,3)(2,3) and (6,11)(6,11).
  • Step 1: Write the formula
    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  • Step 2: Substitute the values
    m=11−36−2=84=2m = \frac{11 - 3}{6 - 2} = \frac{8}{4} = 2
  • Answer: The gradient of the line is **2**.
  • Tip: The bigger the positive gradient, the steeper the uphill climb—so always double-check your signs!