Understanding Gradient in Graphs for 14-Year-Old Students

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:

1. Look at the graph: Find two points on the straight line. Let's call them Point 1 (x₁, y₁) and Point 2 (x₂, y₂).
2. 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.
3. 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.
4. 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.