Equation of a Straight Line for IGCSE Maths
Finding the equation y = mx + c from given information. This subtopic is part of Coordinate Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding equa
What You Need to Know
Finding the equation y = mx + c from given information. This subtopic is part of Coordinate Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding equation of a straight line is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Equation of a Straight Line
The equation of a straight line in IGCSE 0580 is written in the form y = mx + c, where m is the gradient and c is the y-intercept. The y-intercept is where the line crosses the y-axis (when x = 0). Students must be able to identify m and c from a given equation, find the equation from two points or a point and a gradient, and rearrange equations like 2x + 3y = 6 into y = mx + c form.
Step-by-Step Method
- 1
Find the gradient m
Either read it from the graph (rise/run between two points) or calculate m = (y₂ − y₁)/(x₂ − x₁) from two given coordinates.
- 2
Use y = mx + c
Substitute the gradient and one known point (x₁, y₁): y₁ = mx₁ + c. Solve for c.
- 3
Write the full equation
Substitute m and c back into y = mx + c. Do not leave c as an algebraic expression.
- 4
Verify with a second point
Substitute the second point's coordinates into your equation. If it satisfies the equation, your answer is correct.
- 5
Rearrange if asked
Some questions give ax + by = c and ask for y = mx + c form: rearrange by making y the subject.
Worked Example
Question
Find the equation of the line that passes through the points (2, 1) and (5, 7).
Solution
Step 1: Calculate the gradient. m = (7 − 1)/(5 − 2) = 6/3 = 2 Step 2: Substitute into y = mx + c using point (2, 1). 1 = 2(2) + c 1 = 4 + c c = −3 Step 3: Write the equation. y = 2x − 3 Step 4: Verify with (5, 7): y = 2(5) − 3 = 10 − 3 = 7 ✓ Answer: y = 2x − 3
Exam Tips for Equation of a Straight Line
- Always write y = mx + c and substitute — don't try to 'spot' c by eye from the graph unless checking.
- A common mistake: using the coordinates the wrong way round in the gradient formula. Always (y₂−y₁)/(x₂−x₁).
- When the y-intercept is not a whole number (e.g. y = (2/3)x + 7/3), leave it as a fraction.
- Check by substituting BOTH original points into your final equation — if either fails, recheck your gradient calculation.
Practice Questions
Q1: Find the equation of the line with gradient −2 passing through (3, 4).
Show hint
Substitute into y = −2x + c: 4 = −2(3) + c. Solve for c.
Q2: Find the equation of the line through (−1, 5) and (3, −3).
Show hint
m = (−3 − 5)/(3 − (−1)) = −8/4 = −2. Then find c.
Q3: Write 3x + 2y = 10 in the form y = mx + c. State the gradient and y-intercept.
Show hint
Rearrange: 2y = −3x + 10, then y = −(3/2)x + 5.
Frequently Asked Questions
What is equation of a straight line in IGCSE Maths?
Finding the equation y = mx + c from given information.
Is equation of a straight line in the Core or Extended syllabus?
Equation of a Straight Line is part of the Core and Extended syllabus for IGCSE Mathematics 0580.
How do I revise equation of a straight line effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on equation of a straight line rather than trying to cover everything at once.
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