Find the gradients of straightline graphs
The gradient of any line is how much it slopes.
We give a number to define how steep the line is.
A positive gradient means the line is up hill, a negative gradient means the line goes down hill.
To work out the exact gradient of a line, we take a section of it, and see how much its height changed between the start of the section and the end.
On a graph, we can do this really easily and accurately. Pick two points, and look at the difference between their xcoordinates and ycoordinates.
Then, just divide the difference in their ycoordinates, by the difference in their xcoordinates. That’s the gradient.
At either extreme, a gradient of 0 is perfectly horizontal/vertical, and an ‘undefined’ gradient (sometimes called a gradient of infinity) would be a perfectly vertical wall.
Example:
Suppose a linear graph has two coordinates at (2, 5) and (4, 10)
The difference in the xcoordinates is: 42 = 2 The difference in the ycoordinates is: 105 = 5
Gradient = 5/2 = 2.5
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