The tells us how steep a line is, therefore the bigger the gradient the steeper the line is.

A positive gradient is a straight line which slopes up to the right.

A negative gradient is a straight line which slopes down to the right.

## Gradients of special types of lines

Parallel lines have the same gradient

Vertical lines have a gradient which is undefined

Equation $$x = a$$

Horizontal lines have a gradient of zero

Equation $$y = b$$

One of the formulae used to find the gradient of a straight line is:

$Gradient\,of\,a\,slope = \frac{{vertical\,distance}}{{horizontal\,distance}}$

Now try some example questions.

Question

The community centre is getting a new ramp onto their side entrance.

Calculate the gradient of the ramp using the diagram below.

The gradient can be worked out as a simplified fraction or a decimal fraction. Gradient is positive since the line slopes up to the right.

$Gradient = \frac{{vertical\,distance}}{{horizontal\,distance}}$

$= \frac{{26}}{{78}}$

$=\frac{13}{39}$

$=\frac{1}{3}$

or

$= 26 \div 78$

$= 0.333...$

$= 0.3\,(to\,1\,d.p.)$

Question

Calculate the gradient of the line shown below.

Gradient is negative since the line slopes down to the right.

$Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}$

$-\frac{5}{2}$

Question

Calculate the gradient of the slope below.

Gradient is negative since the line slopes down to the right.

$Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}$

$= \frac{{ - 5}}{{20}}$

$= - 5 \div 20$

$= - 0.25\,(to\,2\,d.p.)$

Question

Calculate the gradient of the slope below.

Gradient is positive since the line slopes up to the right.

$Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}$

$= \frac{{10}}{{45}}$

$= \frac{2}{9}$

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