What is a Gradient in a Graph?
The gradient of a graph tells us how steep the line is. It shows how much the line goes up or down as we move along the x-axis (the horizontal line).
Step-by-Step Explanation:
- Look at the graph: Find two points on the straight line. Let's call them Point 1 (x1, y1) and Point 2 (x2, y2).
- Calculate the 'rise': This is the vertical change, which means how much the y-value changes. You find it by subtracting the y-values: rise = y2 - y1.
- Calculate the 'run': This is the horizontal change, which means how much the x-value changes. You find it by subtracting the x-values: run = x2 - x1.
- Find the gradient: The gradient is the ratio of the rise to the run. So, gradient = rise / run = (y2 - y1) / (x2 - x1).
What Does the Gradient Tell Us?
- If the gradient is positive, the line goes up as you move from left to right.
- If the gradient is negative, the line goes down as you move from left to right.
- If the gradient is zero, the line is flat (horizontal).
- If the gradient is undefined (because run is zero), the line is vertical.
Example:
Suppose you have two points on a line: (2, 3) and (5, 11).
- Rise = 11 - 3 = 8
- Run = 5 - 2 = 3
- Gradient = 8 / 3 ≈ 2.67
This means the line rises approximately 2.67 units for every 1 unit it moves to the right.
Summary:
The gradient is a way to measure how steep a line is on a graph. You find it by dividing the change in y by the change in x between two points.