IGCSE · Practice questions · Coordinates and drawing linear graphs

Tables, points, lines.

Six original Cambridge-style questions on coordinates and drawing straight-line graphs, from reading points to using a graph in context.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Choose $x$, work out $y$, plot, rule.

Coordinates: $(x, y)$, across first, then up or down.
Table: substitute each $x$ carefully; brackets round negative numbers.
Pattern check: the $y$ values change by the same amount each step.
Plot and rule: one straight line through every point, across the full range.
Special lines: $x = k$ is vertical, $y = k$ is horizontal.

Recall

[2 marks]

(a) Write down the coordinates of the point that is 3 units to the left of $(2, -1)$ and then 4 units up.

(b) Write down the coordinates of the point where the line $x = -3$ crosses the $x$-axis.

(a) $x = 2 - 3 = -1$ and $y = -1 + 4 = 3$, so $(-1, 3)$. ✓
(b) On the $x$-axis $y = 0$, so $(-3, 0)$. ✓

Calculation

[3 marks]

(a) Complete the table of values for $y = 2x - 3$.

$x$: $-2, -1, 0, 1, 2, 3$

(b) Describe how you would draw the graph for $-2 \le x \le 3$.

(a) $y$: $-7, -5, -3, -1, 1, 3$ (each step of 1 in $x$ adds 2). ✓
(b) Plot $(-2, -7)$, $(-1, -5)$, $(0, -3)$, $(1, -1)$, $(2, 1)$, $(3, 3)$ and draw one ruled straight line from $x = -2$ to $x = 3$. ✓

Calculation

[3 marks]

(Extended) The line $2x + 5y = 10$ is drawn on a grid.

(a) Find the coordinates of the points where it crosses the $x$-axis and the $y$-axis.

(b) Find the value of $y$ on the line when $x = -5$.

(a) $y = 0$: $2x = 10$, so $(5, 0)$. $x = 0$: $5y = 10$, so $(0, 2)$. ✓
(b) $2 \times (-5) + 5y = 10$, so $5y = 20$ and $y = 4$. ✓

Analysis

[2 marks]

Show whether each point lies on the line $y = 2 - 3x$.

(a) $(-3, 11)$ (b) $(4, -9)$

(a) $2 - 3 \times (-3) = 2 + 9 = 11$. This matches, so $(-3, 11)$ is on the line. ✓
(b) $2 - 3 \times 4 = 2 - 12 = -10$, not $-9$, so $(4, -9)$ is not on the line. ✓

Analysis

[3 marks]

$A(-2, 1)$, $B(3, 1)$ and $C(5, 4)$ are three vertices of a parallelogram $ABCD$.

Find the coordinates of $D$.

In a parallelogram $AD$ is the same step as $BC$. ✓
From $B$ to $C$: 2 across and 3 up. ✓
From $A(-2, 1)$, go 2 across and 3 up: $D(0, 4)$. ✓

Analysis

[4 marks]

A taxi charges a fixed $3 plus $2 per kilometre, so the cost of a journey of $x$ km is $C = 2x + 3$ dollars.

(a) Complete a table of values for $x = 0, 2, 4, 6, 8$.

(b) The graph of $C$ against $x$ is drawn. Use the equation to find the length of a journey that costs $13.

(a) $C$: $3, 7, 11, 15, 19$. ✓
(b) $2x + 3 = 13$, so $2x = 10$ and $x = 5$ km (on the graph, go across from 13 on the $C$-axis to the line, then down). ✓
(c) Each extra kilometre always adds the same $2, so the cost goes up in equal steps: the equation is linear. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.

Choose \(x\), work out \(y\), plot, rule.