Page 2: Finding Equations from Graphs

This page focuses on practical applications of straight line concepts, particularly in determining the equation of a line from its graph. The method of calculating gradients using two points on a line is explained in detail.

Definition: The y-intercept is the point where the line crosses the vertical y-axis.

Example: To find the gradient between points (1,1) and (3,5): m = (change in y)/(change in x) = $5-1$/$3-1$ = 2

Highlight: When finding the equation of a line, first calculate the gradient using two points, then identify the y-intercept by looking at where the line crosses the y-axis.

Vocabulary:

• Change in y: The vertical distance between two points
• Change in x: The horizontal distance between two points
• Points: Specific locations on a line represented by coordinates

Page 1: Understanding Straight Line Equations and Gradients

This page introduces the fundamental concepts of straight line graphs and their equations. The coordinate system is explained with the x-axis being horizontal and the y-axis being vertical. The standard form of a straight line equation y = mx + c is thoroughly explored through practical examples.

Definition: A straight line equation follows the format y = mx + c, where m is the gradient and c is the y-intercept.

Example: For the equation y = 3x + 2:

• When x = 0, y = 2
• When x = 1, y = 5
• When x = 2, y = 8

Highlight: The gradient $m$ determines the steepness of the line. A larger gradient creates a steeper line, while a negative gradient means the line slopes downward.

Vocabulary:

• Gradient: The measure of steepness in a line
• Y-intercept: The point where the line crosses the y-axis
• Coordinates: Points on the graph represented as (x,y)