# Recognise Straight Line Graphs

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

Key stage:  KS 3

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

### 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

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:

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!

Example

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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