📈 Cracking Linear Graphs Made Easy!

Linear graphs appear all over your O Level syllabus, science experiments, and even everyday budgeting. Mastering them helps you read trends quickly, check proportionality, and score easy marks in graph-related exam questions.

Key Ideas Behind a Straight Line

A straight-line equation is generally written in the form

y = mx + c

where **m** is the gradient (slope) and **c** is the

y

-intercept. Knowing how to determine **m** and **c** allows you to plot the line accurately and interpret its behavior.

Gradient tells you how steep the line is: $m = \dfrac{\text{rise}}{\text{run}}$ .
$y$ -intercept is the point where the line cuts the $y$ -axis (when $x = 0$ ).

Worked Example: Plotting $y = 2x - 1$

Problem: Draw the graph of

y = 2x - 1

for

-2 \le x \le 3

Step 1: Choose convenient $x$ values (e.g., $-2,-1,0,1,2,3$ ) and calculate $y$ :
$\begin{array}{c|c}x & y=2x-1\\\hline-2 & -5\\-1 & -3\\0 & -1\\1 & 1\\2 & 3\\3 & 5\end{array}$
Step 2: Plot each point $(x, y)$ accurately on graph paper, then use a ruler to join them in a straight line passing through all points.

Practice plotting different gradients and intercepts to strengthen your graph-drawing speed. **Consistency and neatness** earn method marks, so always use a sharp pencil, label axes, and extend your line across the full range.

Key Ideas Behind a Straight Line

Worked Example: Plotting y=2x−1y = 2x - 1y=2x−1

Worked Example: Plotting $y = 2x - 1$