Equations of lines
Cambridge IGCSE Mathematics (0580) · Unit 3: Coordinate geometry · 10 flashcards
Equations of lines is topic 3.3 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 3 — Coordinate geometry , alongside Coordinates and Gradient and length. In one line: The general form is y = mx + c, where 'y' is the dependent variable, 'x' is the independent variable, 'm' is the gradient (slope) of the line, and 'c' is the y-intercept (the point where the line crosses the y-axis).
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 10 flashcards — 3 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 3 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.
The general form of the equation of a straight line, and what do each of the variables represent
The general form is y = mx + c, where 'y' is the dependent variable, 'x' is the independent variable, 'm' is the gradient (slope) of the line, and 'c' is the y-intercept (the point where the line crosses the y-axis).
Questions this Equations of lines deck will help you answer
- › Explain how to determine the gradient of a line given two points on the line, (x1, y1) and (x2, y2).
- › How can you determine if two lines, given in the form ax + by = c, are parallel?
- › Line p has equation y = 4x - 1. Line q is perpendicular to line p and passes through point (8,3). Find the equation of line q.
What is the general form of the equation of a straight line, and what do each of the variables represent?
The general form is y = mx + c, where 'y' is the dependent variable, 'x' is the independent variable, 'm' is the gradient (slope) of the line, and 'c' is the y-intercept (the point where the line crosses the y-axis).
A line has a gradient of 3 and passes through the point (0, 2). What is its equation in the form y = mx + c?
Since the gradient (m) is 3 and it passes through (0, 2), the y-intercept (c) is 2. Therefore, the equation of the line is y = 3x + 2.
Explain how to determine the gradient of a line given two points on the line, (x1, y1) and (x2, y2).
The gradient (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1). This represents the change in y divided by the change in x.
Convert the equation 2x + 3y = 6 into the gradient-intercept form (y = mx + c).
Rearrange the equation: 3y = -2x + 6. Divide by 3 to get y = (-2/3)x + 2. The gradient-intercept form is y = (-2/3)x + 2.
What is the relationship between the gradients of two parallel lines?
Parallel lines have the same gradient. If one line has a gradient of 'm', a parallel line will also have a gradient of 'm'.
Line A has a gradient of 2. What is the gradient of a line perpendicular to Line A?
The gradient of a perpendicular line is the negative reciprocal of the original gradient. The negative reciprocal of 2 is -1/2.
Explain the concept of 'negative reciprocal' in the context of perpendicular lines.
The negative reciprocal of a number is found by inverting the number and changing its sign. If a gradient is 'm', its negative reciprocal is '-1/m'.
Line L passes through (1, 5) and (3, 9). Find the equation of the line in the form y = mx + c.
First, find the gradient: m = (9-5)/(3-1) = 2. Now use one point, say (1,5), and the gradient in y = mx + c, so 5 = 2(1) + c. Thus, c = 3. The equation is y = 2x + 3.
How can you determine if two lines, given in the form ax + by = c, are parallel?
Rearrange both equations into the form y = mx + c. If the 'm' values (gradients) are equal, the lines are parallel.
Line p has equation y = 4x - 1. Line q is perpendicular to line p and passes through point (8,3). Find the equation of line q.
The gradient of line p is 4. The gradient of line q will be -1/4. With point (8,3), 3 = (-1/4)(8) + c. Solving, c = 5. The equation of line q is y = (-1/4)x + 5.
Key Questions: Equations of lines
What is the general form of the equation of a straight line, and what do each of the variables represent?
The general form is y = mx + c, where 'y' is the dependent variable, 'x' is the independent variable, 'm' is the gradient (slope) of the line, and 'c' is the y-intercept (the point where the line crosses the y-axis).
What is the relationship between the gradients of two parallel lines?
Parallel lines have the same gradient. If one line has a gradient of 'm', a parallel line will also have a gradient of 'm'.
Explain the concept of 'negative reciprocal' in the context of perpendicular lines.
The negative reciprocal of a number is found by inverting the number and changing its sign. If a gradient is 'm', its negative reciprocal is '-1/m'.
More topics in Unit 3 — Coordinate geometry
Equations of lines 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 Equations of lines 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
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