Equations of lines
10 flashcards to master Equations of lines
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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'.
About Equations of lines (3.3)
These 10 flashcards cover everything you need to know about Equations of lines for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.
What You'll Learn
- 3 Definitions - Key terms and their precise meanings that examiners expect
- 2 Key Concepts - Core ideas and principles from the 0580 syllabus
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After mastering Equations of lines, explore these related topics:
- 3.2 Gradient and length - 9 flashcards
- 4.1 Angles - 10 flashcards
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