Finding the Gradient

The gradient of a line signifies its steepness; this is a key aspect of understanding and interpreting graphs.
To find the gradient, use the formula: Gradient = (Change in Y) / (Change in X). This is also known as “rise over run.”
When the gradient is positive, the line slopes upwards to the right. The steeper the line, the greater the gradient will be.
A negative gradient indicates a line that slopes downwards to the right. The steeper the slope, the more negative the gradient.
A gradient of zero shows a horizontal line, meaning there is no change in the ‘Y’ values regardless of the ‘X’ values.
To calculate the gradient of a straight line on a graph, choose two points on the line. The difference in ‘Y’ coordinates (rise) divided by the difference in ‘X’ coordinates (run) will give the gradient.
For a curve, you would need to estimate the gradient at a specific point. Draw a tangent (a straight line that just touches the curve at that point) and calculate the gradient of this tangent.
Remember that gradients are used not only in mathematical graphs, but also have real-life applications, such as determining the steepness of a hill or the rate of change in an economic graph.