GraphsDeep Dive

Worked Examples

Part of Gradient & InterceptGCSE Mathematics

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 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 8

Practice

10 questions

Recall

20 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)

Keep building this topic

Read this section alongside the surrounding pages in Gradient & Intercept. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Gradient & Intercept

The gradient of a straight line is calculated by:

  • A. change in x ÷ change in y
  • B. change in y ÷ change in x
  • C. change in y × change in x
  • D. sum of y-values ÷ sum of x-values
1 markfoundation

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?

2 markshigher

Quick Recall Flashcards

What is the x-intercept?
The point where a line crosses the x-axis. Found by setting y = 0.
What is the y-intercept?
The point where a line crosses the y-axis. Found by setting x = 0.

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