Straight line graphs
Cambridge IGCSE Mathematics (0580) · Unit 2: Algebra and graphs · 9 flashcards
Straight line graphs is topic 2.7 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Algebraic notation and manipulation, Equations and Inequalities. In one line: 'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 2 definitions and 2 key concepts — covering the precise wording mark schemes reward. Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line
'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.
Questions this Straight line graphs deck will help you answer
- › What is the relationship between the gradients of two parallel lines?
- › What is the relationship between the gradients of two perpendicular lines?
What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line?
'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.
What does the value 'c' represent in the equation y = mx + c?
'c' represents the y-intercept, the point where the line crosses the y-axis. It's the value of y when x = 0.
Determine the gradient of a line passing through the points (1, 5) and (3, 9).
The gradient (m) is calculated as (change in y) / (change in x). So, m = (9-5) / (3-1) = 4 / 2 = 2. The gradient of the line is 2.
Write the equation of a line with a gradient of -3 that passes through the point (0, 2).
Since the line passes through (0,2), the y-intercept (c) is 2. Using y = mx + c, the equation of the line is y = -3x + 2.
What is the relationship between the gradients of two parallel lines?
Parallel lines have the same gradient. If line 1 has a gradient of m1 and line 2 has a gradient of m2, then for parallel lines, m1 = m2.
What is the relationship between the gradients of two perpendicular lines?
Perpendicular lines have gradients that are negative reciprocals of each other. If line 1 has a gradient of m1 and line 2 has a gradient of m2, then for perpendicular lines, m1 * m2 = -1.
Find the midpoint of the line segment joining the points A(2, 4) and B(6, 8).
The midpoint is found by averaging the x-coordinates and averaging the y-coordinates. Midpoint = ((2+6)/2, (4+8)/2) = (4, 6).
Calculate the distance between the points (1, 2) and (4, 6). Give your answer to 2 decimal places.
Use the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Distance = sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.00.
A line has the equation 2y + 4x = 8. What is its gradient?
Rearrange the equation to the form y = mx + c. 2y = -4x + 8, so y = -2x + 4. The gradient, m, is -2.
Key Questions: Straight line graphs
What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line?
'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.
What does the value 'c' represent in the equation y = mx + c?
'c' represents the y-intercept, the point where the line crosses the y-axis. It's the value of y when x = 0.
Tips to avoid common mistakes in Straight line graphs
- ● When calculating a gradient, carefully consider the scale of each axis; the gradient is the change in y divided by the change in x, considering the respective scale.
More topics in Unit 2 — Algebra and graphs
Straight line graphs sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Straight line graphs deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Straight line graphs deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Space to flip • ←→ to navigate • Esc to close
You're on a roll!
You've viewed 10 topics today
Create a free account to unlock unlimited access to all revision notes, flashcards, and study materials.
You're all set!
Enjoy unlimited access to all study materials.
Something went wrong. Please try again.
What you'll get:
- Unlimited revision notes & flashcards
- Track your study progress
- No spam, just study updates