The gradient 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.

**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.

\[Gradient\, = \frac{{vertical\,distance}}{{horizontal\,distance}}\]

\[= \frac{{10}}{{45}}\]

\[= \frac{2}{9}\]