### by Mark Dawes (November 2019)

Desmos can be used to draw pictures that include straight lines and curves. See www.desmos.com/art for some ideas. Here are a few of the techniques that might be helpful.

### Getting started

Go to www.desmos.com and click on ‘Start Graphing’.

It is worth signing in (it’s quick and easy to create an account – particularly if you already have Gmail) because then you can save your work.

To change the title of your work, click on the words “Untitled Graph”. Then save it.

Type the equation of a line or curve on the left-hand side and see the graph appear on the right.

The on-screen keyboard can be opened by clicking in the bottom left of the screen.

### Drawing segments of lines

If you draw the line y = 2x – 1 it will fill the screen in both directions. If you only want part of the line you can put in a domain or a range. After putting in the equation of the line you use the curly brackets, known as ‘braces’, that look like this: { }

The easy way to get ≤ is to type <=.

### Other shapes

You might find other equations helpful, for example:

### Circles

This gives you a circle with centre (1, 4) and radius of 3 (the square root of 9).

See what happens if you put a number in front of the x or the y (just one of them).

### Coloured regions

If you use an inequality symbol instead of the equals sign it shades a region (try it with a circle!).

The next image shows the difference between using < and ≤ as well as showing the region being restricted in the x and the y direction.

### Translating a graph

To translate (move) a graph to the right by 2, change x into (x – 2).

To translate a graph up by 3, change y into (y – 3).

### Polishing your design

To change the colour of a line, click on the cog-wheel and then on the coloured dot next to the equation.

To make the lines thicker (this might not be a good thing) you can go to ‘graph settings’ and select ‘Projector Mode’. When you have finished your picture you can remove the grid and the x-axis and y-axis here too.

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