EDEXCEL GCSE FOUNDATION MATHS - What are Parallel Graphs

Parallel Graphs: A Foundation Maths Tutorial

What are Parallel Lines?

Imagine two train tracks running side-by-side. They never intersect, and the distance between them always stays the same. This is similar to parallel lines in mathematics. Parallel lines are lines that never intersect, no matter how far they extend. They always maintain the same distance apart.

How to Identify Parallel Lines

• Same Gradient: The most crucial aspect of parallel lines is that they have the same gradient. The gradient measures the steepness of a line.
• Different Y-intercepts: Parallel lines can have different y-intercepts. The y-intercept is the point where the line crosses the y-axis.

Examples:

• Line 1: Equation: y = 2x + 3
• Line 2: Equation: y = 2x - 1

Both lines have a gradient of 2, indicating they are parallel. They have different y-intercepts (3 and -1, respectively).

Understanding the Gradient

The gradient (often represented by the letter 'm') tells you how steep the line is. It is calculated as:

Gradient (m) = (Change in y) / (Change in x)

Visual Representation:

• Parallel lines will have the same angle of inclination relative to the x-axis.
• They will always remain the same distance apart, no matter how far they are extended.

Real-World Applications

Parallel lines are found everywhere in the real world:

• Railroad Tracks: The two rails are parallel lines.
• Lanes on a Road: The lanes of a road are parallel lines.
• Horizontal Lines on a Grid: The horizontal lines on a grid are parallel to each other.

Summary:

• Parallel lines never intersect.
• They have the same gradient.
• They can have different y-intercepts.
• They have the same angle of inclination.

Understanding parallel lines is crucial for understanding various concepts in geometry, algebra, and calculus. So, take your time to practice identifying and understanding these important lines.