Sectieoverzicht
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How to find the gradient of a line
Gradient is a measure of the steepness of a line.
We use the formula \(m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\) to calculate the gradient or slope between any two points on a straight line.
Example
Find the gradient between the points \(A(5,2)\) and \(B(9,-3)\).
\({m}_{AB}=\frac{-3-2}{9-5}=\frac{-5}{4}\)
Note: If you start with \({y}_{2}\) in the numerator then you must start with \({x}_{2}\) in the denominator. If you change the order you start with then the answer will not be correct.
Watch the next video for further explanation on finding the gradient.
If you would like more practise finding the gradient between two points, visit the interactive simulation called Calculating gradient. Choose any two points on the Cartesian plane and click on "show calculation" to see how the gradient is worked out.-
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Parallel and perpendicular lines
Parallel lines are always the same distance apart. This means that on the Cartesian plane, parallel lines have the same gradient. So to show that two lines are parallel we simply need to show that their gradients are equal.
Perpendicular lines lie at \({90}^\circ\) to each other. If two lines are perpendicular then the product of their gradients is \(-1\).
In the next video you will go over a few examples using the gradients of parallel and perpendicular lines.
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