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Straight-line graphs

The equations of straight-line graphs are easy to recognise. They will look like one of these:

  • \(\text{x = a}\)
  • \(\text{y = b}\)
  • \(\text{y = cx + d}\)

where a, b, c and d represent numbers.

For example, \(\text{x = 3}\), \(\text{y = -7}\), \(\text{y = 5x + 11}\)

Lines in the form \(\text{x = a}\) will always be vertical lines.

Example

This is the line \(\text{x = 3}\):

A graph with an x and y axis from -8 to 8 showing a solid vertical line with the label x = 3.

Similarly, lines in the form \(\text{y = b}\) will always be horizontal lines.

y = cx + d

For lines in the form \(\text{y = cx + d}\), you will normally be asked to complete a table of values before you draw the graph.

Example

Let’s look at the line \(\text{y = x + 3}\).

We need to complete the table to find the missing values.

\(\text{x}\)-2-1012
\(\text{y = x + 3}\)23
\(\text{x}\)
-2
-1
0
1
2
\(\text{y = x + 3}\)
2
3

When \(\text{x = -2}\):

\(\text{y = -2 + 3 = 1}\)

When \(\text{x = 1}\):

\(\text{y = 1 + 3 = 4}\)

When \(\text{x = 2}\):

\(\text{y = 2 + 3 = 5}\)

So our completed table of values will look like this:

\(\text{x}\)-2-1012
\(\text{y = x + 3}\)12345
\(\text{x}\)
-2
-1
0
1
2
\(\text{y = x + 3}\)
1
2
3
4
5

To draw this graph, we need to think of the values in this table as coordinates.

So the first point will have coordinates \(\text{(-2,~1)}\), the second will have coordinates \(\text{(-1,~2)}\) etc.

We then join up our points with a straight line.

A graph with an x and y axis from 8 to 8 showing a solid slanted line crossing x-3 and y3.

Question

Complete the table and draw the graph of \(\text{y = 3x - 1}\)

\(\text{x}\)-10123
\(\text{y = 3x - 1}\)-45
\(\text{x}\)
-1
0
1
2
3
\(\text{y = 3x - 1}\)
-4
5