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Recognise Straight Line Graphs

In this worksheet, students will be able to link straight line graphs with sequences and recognise them.

'Recognise Straight Line Graphs' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

Curriculum subtopic:   Use Linear Equations (Two Variables) and Gradients

Difficulty level:  

Worksheet Overview

In this activity, we will be looking at how sequences link to straight line graphs.


Let's take the sequence:

2, 4, 6, 8 ,10, .........

We can see that this is the 2 times table, so the rule for this is 2n


What about 

3, 5, 7, 9, 11, ........

This still goes up in 2's so the rule is 2n, but each term is not 2, 4, 6 etc

Each term is 1 more than the 2 times table.

Therefore, our rule for this one is 2n + 1


woman thinking


We can apply this rule to recognising and drawing straight line graphs.

We use y and x, but it is just a sequence of coordinates which join to form a straight line.


See the graph of y = 2x + 1 below:


gradient of a line on a grid


As in the sequence, the line starts at y = 1 and goes up in 2's (that is 1 across, 2 up)


We can recognise a straight line graph because it goes up or down by a constant value (2 in this case).

If the x was x2 or x3 etc it would not be constant, so would form a curve.


Let's look at a typical question!



Which of the equations below form a straight line graph?

y = 3x - 5                                y = 2x + x2



y = 3x - 5 is the answer as it goes up by 3, which is constant.

The x2 term in the other equation makes the graph form a curve.


Let's have a go at some questions!

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