Drawing Graphs of Straight Lines

This section focuses on drawing graphs coordinate geometry GCSE questions and answers.

Methods for Drawing Straight Line Graphs

The page outlines different approaches to drawing straight line graphs:

1. Using the y = mx + c form
2. Plotting the y-intercept and using the gradient
3. Finding x and y intercepts from the ax + by = c form

Example: A detailed worked example shows how to draw the lines y = 3x - 1 and 5x - 3y = 15 on the same set of axes.

The step-by-step process for plotting these lines is explained, including finding intercepts and using the gradient to plot additional points.

Perpendicular Lines

This page covers the concept of perpendicular lines in GCSE coordinate geometry questions and answers.

Understanding Perpendicular Lines

Definition: Perpendicular lines are lines that intersect at a right angle (90°).

The relationship between the gradients of perpendicular lines is explained:

Highlight: For two lines to be perpendicular, the product of their gradients must equal -1: m₁ × m₂ = -1.

Worked Example

The page includes a detailed worked example:

Example: Given a line with equation y = 2x + 2, find the equation of a perpendicular line passing through the point $2, -3$.

The solution demonstrates how to:

1. Find the perpendicular gradient
2. Use the point-slope form to determine the equation
3. Simplify to get the final answer: y = -½x - 2

This comprehensive guide provides students with the necessary tools to tackle GCSE coordinate geometry exam questions confidently.

Coordinates and Straight Lines

This page introduces fundamental concepts in coordinate geometry GCSE questions and answers.

Coordinates and Gradients

The page explains how to work with coordinates and calculate gradients between two points.

Definition: The gradient between two points (x₁, y₁) and (x₂, y₂) is calculated using the formula: $y₂ - y₁$ / $x₂ - x₁$.

Example: For points $-3, 5$ and (2, 8), the gradient would be $8 - 5$ / $2 - (-3)$ = 3/5.

Midpoint and Distance

The concept of midpoint and distance between two points is introduced.

Highlight: The distance between two points is found using the Pythagorean theorem: √$(x₂ - x₁)² + (y₂ - y₁)²$.

Straight Line Equations

The page covers the general equation of a straight line: y = mx + c.

Vocabulary: In the equation y = mx + c, 'm' represents the gradient, and 'c' is the y-intercept.

A worked example demonstrates how to find the equation of a line parallel to y = 4x + 5 passing through the point $-2, 5$.