Straight-Line Graphs: Gradients

Gradients express the steepness of a line on a graph.
The gradient of a straight line is a continuous constant that doesn’t change along the line.
A positive gradient means a line is ascending from left to right.
A negative gradient means a line is descending from left to right.
The steepness of the slope equals the value of the gradient. High absolute values indicate steep slopes whereas low absolute values indicate gentle slopes.
Gradients also indicate direction - positive gradients increase in the right direction whereas negative gradients decrease.

To calculate the gradient of a straight line, use the formula: Gradient = (Change in Y) / (Change in X).
In the formula, ‘Change in Y’ represents the vertical difference between two points on the line and ‘Change in X’ represents the horizontal difference.
This formula is often remembered as the rise over run formula.
It is also common to represent it as m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two distinct points on the line.

A zero gradient means the line is flat and horizontal.
An undefined or infinite gradient means the line is vertical.
A unit gradient is when the line rises or descends by one unit vertically for each unit travelled horizontally.

Firs, you need to understand the slope-intercept equation of a line, y = mx + c, where m is the gradient and c is the y-intercept.
The y-intercept is where the line crosses the y-axis
To plot a line with a specific gradient, start by marking the y-intercept on the y-axis. Then, follow the gradient to draw the line:
- If the gradient is positive (+m), go up m units and right 1 unit from the y-intercept.
- If the gradient is negative (-m), go down m units and right 1 unit from the y-intercept.