Gradients of Straight Lines: A Worksheet for UK Maths Students

📚 Topic Summary

The gradient of a straight line is a measure of its steepness. It tells us how much the y-value changes for every unit change in the x-value. A positive gradient indicates an increasing line, while a negative gradient indicates a decreasing line. We calculate it using the formula: gradient = (change in y) / (change in x). Understanding gradients is crucial for graphing linear equations and solving related problems. This worksheet will help you to solidify your understanding of gradients and practice your skills!📈

📏 Part A: Vocabulary

Match the following terms with their definitions:

1. Term: Gradient
2. Term: Y-intercept
3. Term: Coordinates
4. Term: Linear Equation
5. Term: Rise over Run

1. Definition: The point where the line crosses the y-axis.
2. Definition: A way to calculate the gradient, where rise is the vertical change and run is the horizontal change.
3. Definition: A relationship between variables that, when plotted on a graph, forms a straight line.
4. Definition: A measure of the steepness of a line.
5. Definition: A set of values that show an exact position on a coordinate plane.

✍️ Part B: Fill in the Blanks

Complete the following paragraph using the words provided: positive, negative, zero, undefined, steepness

The gradient of a line describes its __________. A line with a __________ gradient slopes upwards from left to right. A line with a __________ gradient slopes downwards from left to right. A horizontal line has a __________ gradient, while a vertical line has an __________ gradient.

🤔 Part C: Critical Thinking

Explain in your own words how the gradient of a line affects its appearance on a graph. Use examples to illustrate your answer.