CIE IGCSE Mathematics (0580) Gradient of linear graphs Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Gradient of linear graphs Study Notes
LEARNING OBJECTIVE
- Gradient of Linear Graphs (From a Grid)
Key Concepts:
- Gradient of Linear Graphs
Gradient of Linear Graphs (From a Grid)
Gradient of Linear Graphs (From a Grid)
The gradient (or slope) of a straight line shows how steep the line is. It is calculated using a graph by comparing the vertical and horizontal change between two points on the line.
Gradient is found using the formula:
\( \text{Gradient (m)} = \frac{\text{Vertical change (rise)}}{\text{Horizontal change (run)}} \)
\( \text{Gradient (m)} = \frac{\mathrm{y_2-y_1}}{\mathrm{x_2-x_1}} \)
Steps to Find the Gradient from a Grid:
- Pick two clear points on the line (with whole number coordinates).
- Count how many units up/down (rise) and right (run) between the points.
- Apply the gradient formula.
Key Points:
- A line going up from left to right has a positive gradient.
- A line going down from left to right has a negative gradient.
- A horizontal line has a gradient of 0.
- A vertical line has an undefined gradient.
Example:
Find the gradient of a line that passes through the points (1, 2) and (4, 5) on a grid.
▶️ Answer/Explanation
Rise = \( 5 – 2 = 3 \), Run = \( 4 – 1 = 3 \)
\( \text{Gradient} = \frac{3}{3} = 1 \)
Answer: Gradient = 1
Example:
A straight line goes through (2, 5) and (5, 2). Find its gradient.
▶️ Answer/Explanation
Rise = \( 2 – 5 = -3 \), Run = \( 5 – 2 = 3 \)
\( \text{Gradient} = \frac{-3}{3} = -1 \)
Answer: Gradient = -1
Example:
A horizontal line passes through the points (0, 4) and (5, 4). What is its gradient?
▶️ Answer/Explanation
Rise = \( 4 – 4 = 0 \), Run = \( 5 – 0 = 5 \)
\( \text{Gradient} = \frac{0}{5} = 0 \)
Answer: Gradient = 0