2.7

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.

Key definition

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

Definition Flip

What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line?

Answer Flip

'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.

Definition Flip

What does the value 'c' represent in the equation y = mx + c?

Answer Flip

'c' represents the y-intercept, the point where the line crosses the y-axis. It's the value of y when x = 0.

Example: in y = 2x + 3, the line crosses the y-axis at y = 3.
Key Concept Flip

Determine the gradient of a line passing through the points (1, 5) and (3, 9).

Answer Flip

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.

Key Concept Flip

Write the equation of a line with a gradient of -3 that passes through the point (0, 2).

Answer Flip

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.

Key Concept Flip

What is the relationship between the gradients of two parallel lines?

Answer Flip

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.

Key Concept Flip

What is the relationship between the gradients of two perpendicular lines?

Answer Flip

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.

Key Concept Flip

Find the midpoint of the line segment joining the points A(2, 4) and B(6, 8).

Answer Flip

The midpoint is found by averaging the x-coordinates and averaging the y-coordinates. Midpoint = ((2+6)/2, (4+8)/2) = (4, 6).

Key Concept Flip

Calculate the distance between the points (1, 2) and (4, 6). Give your answer to 2 decimal places.

Answer Flip

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.

Key Concept Flip

A line has the equation 2y + 4x = 8. What is its gradient?

Answer Flip

Rearrange the equation to the form y = mx + c. 2y = -4x + 8, so y = -2x + 4. The gradient, m, is -2.

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2.6 Graphs of functions 2.8 Functions

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.

Example: in y = 2x + 3, the line crosses the y-axis at y = 3.

Tips to avoid common mistakes in Straight line graphs

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.

straight line linear gradient slope y-intercept y = mx + c parallel perpendicular equation of line midpoint distance between points

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.

What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line
What does the value 'c' represent in the equation y = mx + c

Related Mathematics guides

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