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Questions and Answers
What is the gradient of a straight line that passes through the points (2, 3) and (4, 7)?
What is the gradient of a straight line that passes through the points (2, 3) and (4, 7)?
What is the equation of a straight line that passes through the point (3, 2) and has a gradient of 2?
What is the equation of a straight line that passes through the point (3, 2) and has a gradient of 2?
What is the equation of a straight line that passes through the points (1, 3) and (2, 5)?
What is the equation of a straight line that passes through the points (1, 3) and (2, 5)?
What is the gradient of a straight line that passes through the point (2, 5) and is parallel to the line y = 3x - 2?
What is the gradient of a straight line that passes through the point (2, 5) and is parallel to the line y = 3x - 2?
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What is the equation of a straight line that passes through the point (4, 3) and is perpendicular to the line y = 2x + 1?
What is the equation of a straight line that passes through the point (4, 3) and is perpendicular to the line y = 2x + 1?
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The graph of the equation y = 2x - 3 has a negative gradient.
The graph of the equation y = 2x - 3 has a negative gradient.
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Two perpendicular lines have gradients that multiply to give -1.
Two perpendicular lines have gradients that multiply to give -1.
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The equation of a straight line that passes through the points (1, 2) and (2, 3) is y = x + 1.
The equation of a straight line that passes through the points (1, 2) and (2, 3) is y = x + 1.
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A line with a gradient of 0 is a horizontal line.
A line with a gradient of 0 is a horizontal line.
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The graph of the equation x = 2 is a straight line with a gradient of undefined.
The graph of the equation x = 2 is a straight line with a gradient of undefined.
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Study Notes
Gradient and Equation of a Straight Line
- The gradient of a straight line through points (2, 3) and (4, 7) is calculated as the change in y over the change in x, resulting in a gradient of 2.
- The equation of a straight line through point (3, 2) with a gradient of 2 is expressed as y = 2x - 4 after applying the point-slope formula.
- For the points (1, 3) and (2, 5), the gradient is 2, leading to the equation of the line being y = 2x + 1.
Properties of Gradient
- A straight line parallel to y = 3x - 2 will have the same gradient of 3; therefore, the gradient of a line through (2, 5) that is parallel to this line is also 3.
- The gradient of a line perpendicular to the line represented by y = 2x + 1 is the negative reciprocal of 2, resulting in a gradient of -1.
Characteristics of Lines and Gradients
- The equation y = 2x - 3 demonstrates a positive gradient of 2, emphasizing that a negative gradient would indicate a downward slope.
- Perpendicular lines feature gradients that multiply to -1, confirming the relationship between their inclinations.
- A line with a gradient of 0 is horizontal, indicating no vertical change regardless of horizontal movement.
- The equation x = 2 represents a vertical line with an undefined gradient, characteristic of vertical lines where x remains constant while y varies.
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Description
Test your understanding of linear graphs with this challenging quiz, designed for top set Year 9 students. Covers graph plotting, gradients, and equations. Are you ready to prove your skills?
