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The gradient of a straight line is a measure of the slope of the line. The larger the value of the
gradient, the steeper the slope.

Finding the gradient of a line can be referred to as finding slope.

If you know either the endpoints, or even just 2 different points on a straight line.

Say

Then the gradient/slope of the straight line, usually labelled

This is often referred to as the "slope formula".

It doesn’t matter which of the co-ordinates is **( x1,y1)** or

Whether or not the gradient is positive or negative, tells us the direction of the straight line.

A line with negative gradient, such as **-4**, slopes downward from left
to right. **\**

A line with positive gradient, such as **4**, slopes upward from left to
right. **/**

\bf{\frac{6 \space - \space 2}{3 \space - \space 1}} = \bf{\frac{4}{2}} =

The Gradient

\bf{\frac{2 \space - \space 5}{8 \space - \space 5}} = \bf{\frac{-3}{3}} = -

Another way to work out the gradient of a straight line is with the "tan" button on a calculator.

When you know the size of the angle that a straight line makes with the positive direction of the
** x**-axis.

The line **L** in the picture above, makes an angle of **θ** with the positive direction of
the ** x**-axis.

When you know the value of this angle, the gradient of a line such as

The gradient of a horizontal line is always **0**.

As it is a flat line with no slope.

The gradient of a vertical line is classed as undefined.

A vertical line isn’t flat, but as it's pointing straight up, it isn’t really sloping in any
particular direction either.

In the image above, line A is Horizontal, and line B is vertical.

The gradient of both lines:

\bf{\frac{3 \space - \space 3}{4 \space - \space 1}} = \bf{\frac{0}{3}} =

\bf{\frac{4 \space - \space 2}{6 \space - \space 6}} = \bf{\frac{2}{0}} = undefined

Lines that are parallel to each other have the same gradient, as they slope the same way.

Lines A and B in this example are both sloping the same way. So the gradient of each line should be the same as the other.

Gradients:

\bf{\frac{5 \space - \space 1}{4 \space - \space 1}} = \bf{\frac{4}{3}}

\bf{\frac{5 \space - \space 1}{6 \space - \space 3}} = \bf{\frac{4}{3}}

If two lines are perpendicular, that is at a right angle to each other, then the gradients multiplied
together will be equal to  -**1**.

Now:

-\bf{\frac{3}{2}} × \bf{\frac{2}{3}} = -\bf{\frac{6}{6}} = -

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