Drawing Linear Graphs — GCSE Maths Tutorial, Worked Examples & Practice

Revise Drawing Linear Graphs (completing tables of values and plotting y = mx + c and ax + by = c straight lines) within Algebra — Coordinate Geometry, aligned to Edexcel, AQA & OCR GCSE (9–1) and International GCSE Maths. The interactive practice tool at the top of this page includes 30 self-marking practice questions across 3 structured skill steps, with instant diagnostic feedback and full worked solutions.

Step 1 of 310 interactive practice questions

Tables of Values & Plotting y = mx + c

Completing tables of values and plotting straight-line graphs across 4 quadrants

Key Method & Revision Notes

To draw a straight-line graph such as $y = 2x - 1$ across a grid from $x = -2$ to $x = 3$:
$x$ — $-2$ — $-1$ — $0$ — $1$ — $2$ — $3$
$y$ — $-5$ — $-3$ — $-1$ — $1$ — $3$ — $5$
3 Steps for Full Marks:
1. Start with positive $x$ values ($0, 1, 2, 3$) — they are easiest! Notice the $y$-values step up by the gradient ($+2$) each time.
2. Plot each $(x, y)$ pair with a neat cross ($\times$).
3. Join with a single ruled straight line right across the grid — if one point doesn't sit on the straight line, re-check your arithmetic for that point!

Worked Example

Question:

Complete the table of values for $y = 3x - 2$ for $x = -1, 0, 1, 2$.

Step-by-Step Solution:

Start from $x = 0$: $y = -2$.

At $x = 1$: $y = 3(1) - 2 = 1$.

At $x = 2$: $y = 3(2) - 2 = 4$.

At $x = -1$: $y = 3(-1) - 2 = -5$.

Plot $(-1, -5), (0, -2), (1, 1), (2, 4)$ and join with a ruler.

y = -5, -2, 1, 4

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 2 of 310 interactive practice questions

Negative & Fractional Gradients

Substituting negative x-values safely into y = c - mx and fractional-gradient lines

Key Method & Revision Notes

Watch out for negative signs when substituting negative $x$-values into lines with negative gradients like $y = 4 - 2x$ (or $y = -2x + 4$):
Classic Negative Sign Trap ($x = -2$ in $y = 4 - 2x$):
Put brackets around $x$: $$y = 4 - 2(-2) = 4 + 4 = \mathbf{8} \quad (\text{NOT } 0!)$$

Worked Example

Question:

Complete the values of $y$ for $y = 5 - 2x$ when $x = -2$, $x = 0$, and $x = 3$.

Step-by-Step Solution:

• At $x = -2$: $y = 5 - 2(-2) = 5 + 4 = \mathbf{9}$.

• At $x = 0$: $y = 5 - 0 = \mathbf{5}$.

• At $x = 3$: $y = 5 - 2(3) = \mathbf{-1}$.

y = 9, 5, -1

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 3 of 310 interactive practice questions

Implicit Lines (ax + by = c) & Intercepts

Drawing straight lines of the form ax + by = c using the cover-up intercept method

Key Method & Revision Notes

When an equation is written in implicit form like $2x + 3y = 12$, the fastest way to draw it is the Cover-Up (Intercept) Method:
1. Find the $y$-intercept (set $x = 0$): Cover up $2x \implies 3y = 12 \implies y = 4 \rightarrow$ plot $(0, 4)$.
2. Find the $x$-intercept (set $y = 0$): Cover up $3y \implies 2x = 12 \implies x = 6 \rightarrow$ plot $(6, 0)$.
3. Draw a straight ruled line passing through $(0, 4)$ and $(6, 0)$!

Worked Example

Question:

Find the coordinates where $3x + 5y = 15$ crosses both axes.

Step-by-Step Solution:

1. Put $x = 0$: $5y = 15 \implies y = 3 \rightarrow (0, 3)$ on the $y$-axis.

2. Put $y = 0$: $3x = 15 \implies x = 5 \rightarrow (5, 0)$ on the $x$-axis.

Plot $(0, 3)$ and $(5, 0)$ and draw the straight line through both points.

(0, 3) and (5, 0)

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Drawing Linear Graphs — GCSE Maths Tutorial, Worked Examples & Practice

Tables of Values & Plotting y = mx + c

Key Method & Revision Notes

Worked Example

Negative & Fractional Gradients

Key Method & Revision Notes

Worked Example

Implicit Lines (ax + by = c) & Intercepts

Key Method & Revision Notes

Worked Example

Related GCSE Maths Topics (Coordinate Geometry)