Podcast
Questions and Answers
What is the formula to calculate the gradient of a straight line?
What is the formula to calculate the gradient of a straight line?
- Gradient = Change in x / Change in y
- Gradient = y^2 / x^2
- Gradient = Change in y / Change in x (correct)
- Gradient = y / x
If a straight line has a gradient of 0, what does that indicate about the line?
If a straight line has a gradient of 0, what does that indicate about the line?
- It is undefined.
- It is increasing.
- It is horizontal. (correct)
- It is vertical.
Which of the following would result in a negative gradient?
Which of the following would result in a negative gradient?
- The line is perpendicular to the x-axis.
- The line falls as it goes from left to right. (correct)
- The line rises as it goes from left to right.
- The line remains constant.
How does the steepness of a line relate to its gradient?
How does the steepness of a line relate to its gradient?
What can be inferred if two lines have the same gradient?
What can be inferred if two lines have the same gradient?
Flashcards
Gradient of a straight line
Gradient of a straight line
The change in the vertical (y) coordinates divided by the change in the horizontal (x) coordinates. It measures the steepness and direction of a line.
Gradient of a horizontal line
Gradient of a horizontal line
A horizontal line has a gradient of zero, indicating that there is no change in the vertical direction.
Negative gradient
Negative gradient
A line with a negative gradient falls as it moves from left to right, meaning the y-coordinate decreases as the x-coordinate increases.
Steepness and gradient
Steepness and gradient
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Parallel lines and gradient
Parallel lines and gradient
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Study Notes
Gradient of a Straight Line
- The gradient of a straight line is calculated using the formula: Gradient = (Change in y)/(Change in x)
- This formula represents the vertical change (rise) divided by the horizontal change (run) between any two points on the line.
Gradient of 0
- A straight line with a gradient of 0 is a horizontal line.
- This means it has no vertical change, resulting in a zero value for the numerator in the gradient formula.
Negative Gradient
- A straight line has a negative gradient when it slopes downwards from left to right.
- This means the change in y is negative (the line goes down) while the change in x is positive (the line goes to the right).
Steepness and Gradient
- The steepness of a line is directly proportional to its gradient.
- A larger absolute value of the gradient means a steeper line.
- For example, a line with a gradient of 2 is steeper than a line with a gradient of 1.
Same Gradient
- If two lines have the same gradient, they are parallel.
- This means they have the same slope and will never intersect.
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Description
Test your understanding of the gradient of a straight line with this quiz. Answer questions about gradient calculations, implications of zero gradient, negative gradients, and relationships between lines with equal gradients. Perfect for students learning about linear equations and geometry.
