Worked examples
Question
Find the gradient of the line joining the points A(5, 8) and B(3, 10)
\(A({x_1},{y_1})\,and\,B({x_2},{y_2})\)
\(A(5,8)\,and\,B(3,10)\)
\({m_{AB}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\)
\({m_{AB}} = \frac{{10 - 8}}{{3 - 5}}\)
\({m_{AB}} = \frac{{10 - 8}}{{3 - 5}}\)
\({m_{AB}} = \frac{2}{{ - 2}} = - 1\)
Now try the sample question below.
Question
Find the gradient of the line below:
To calculate the gradient of this line using the formula, first pick two coordinates that lie on the line.
Any two points can be chosen but for the example below the points (2,7) and (9,3) have been selected.
If different points are chosen the answer will still be the same.
\(({x_1},{y_1})\,and\,({x_2},{y_2})\)
\((2,7)\,and\,(9,3)\)
\(m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\)
\(m = \frac{{3 - 7}}{{9 - 2}}\)
\(m = \frac{{ - 4}}{7}\)
More guides on this topic
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates
