This deep dive covers Worked Examples within Gradient & Intercept for GCSE Mathematics. Revise Gradient & Intercept in Graphs for GCSE Mathematics with 10 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Examples
Example 1: Finding Gradient from Points
Find the gradient of the line through (2, 5) and (6, 11)
Solution:
Gradient = (y₂ - y₁)/(x₂ - x₁) = (11 - 5)/(6 - 2) = 6/4 = 1.5
Example 2: Finding All Intercepts
For y = 4x - 8, find both intercepts
Solution:
- Y-intercept: Set x = 0 → y = 4(0) - 8 = -8 → Point (0, -8)
- X-intercept: Set y = 0 → 0 = 4x - 8 → 4x = 8 → x = 2 → Point (2, 0)
Example 3: Interpreting Gradient
A line has gradient -3. What does this mean?
- The gradient is negative, so the line slopes downward
- For every 1 unit right, the line goes 3 units down
- The line is quite steep (|3| is relatively large)
Practice questions for Gradient & Intercept
The gradient of a straight line is calculated by:
A graph shows the distance (km) travelled by a car plotted against time (hours). The line has gradient 80. What does the gradient represent in this context?