Cambridge IGCSE Maths (0580) · Topic 3: Coordinate geometry · 3.5
Equation of a Straight Line questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
The equation of a line is \(y = 9 - 5x\).
Write down (a) its gradient (b) the coordinates of the point where it crosses the \(y\)-axis.
Answer: (a) \(-5\) (b) \((0, 9)\)
A line has gradient \(-2\) and crosses the \(y\)-axis at \((0, 5)\).
Write down its equation.
Answer: \(y = -2x + 5\)
Write down the equation of the vertical line through \((-4, 6)\).
Answer: \(x = -4\)
Write down the equation of the straight line with
(a) gradient 2 and \(y\)-intercept 5
(b) gradient \(-\frac{1}{2}\) and \(y\)-intercept 3.
Answer: (a) \(y = 2x + 5\) (b) \(y = -\frac{1}{2}x + 3\)
The graph of a straight line is drawn on a grid. The line passes through the grid points \((1, 4)\) and \((3, 10)\). Find the equation of the line in the form \(y = mx + c\).
Answer: \(y = 3x + 1\)
Write \(2y = 6x - 8\) in the form \(y = mx + c\) and write down the gradient.
Answer: \(y = 3x - 4\), gradient \(3\)
Extended content, for Papers 2 and 4. Core students can skip these.
Find the gradient and the \(y\)-intercept of the line \(2y = 6x + 10\).
Answer: Gradient \(3\), \(y\)-intercept \(5\)
Find the gradient of the line \(3x + 4y = 12\).
Answer: \(-\frac{3}{4}\)
Find the equation of the line through \((1, 4)\) and \((3, 10)\).
Answer: \(y = 3x + 1\)
Find the equation of the line through \((-2, 7)\) and \((4, -5)\).
Answer: \(y = -2x + 3\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Equation of a Straight Line is on both tiers (syllabus 3.5), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 3 (Coordinate geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision