How to Discovering Patterns: Using Graphs to Find Rules

A graph shows a pattern as a shape, and the rule behind it can be read straight off the points: find how much y changes for each step in x, then what y is when x is zero. Below: the method step by step, two worked examples, and practice questions.

They show us how numbers change and help us see patterns. Let’s learn how to look at graphs and find the rules that make these patterns!

Step-by-step Guide to Using Graphs to Find Rules:

1. Look at the Graph: 

Is it a line that goes up or down? Or is it a bunch of dots? This will give you a clue about the pattern.

2. Check the Spaces: 

See how much the line goes up or down as you move from one dot to the next. This can tell you the rule of the pattern.

3. Starting Point: 

Find where the line starts. This is often where the line meets the bottom line of the graph.

4. Guess the Rule: 

Using the starting point and the spaces between the dots, try to guess the rule. For example, if the line starts at 2 and goes up by 2 every time, the rule might be “start at 2 and add 2.”

5. Test Your Guess: 

Pick some dots on the graph and see if they follow your rule. If they do, you’ve probably found the right rule!

Example 1: 

Imagine a line that starts at 2 and goes up by 2 every time. The dots on the graph might be at (1,2), (2,4), and (3,6). The rule is “start at 2 and add 2.”

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Example 2: 

If there’s a line that starts at 5 and goes down by 1 each time, the dots might be at (1,5), (2,4), and (3,3). The rule is “start at 5 and take away 1.”

Practice Questions: 

1. If a line starts at 3 and goes up by 3 each time, where will the dot be when it’s at 2?

2. Imagine a line that starts at 4 and goes down by 2 each time. Where will the dot be when it’s at 3?

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Answers: 

1. The dot will be at (2,6).

2. The dot will be at (3,2).

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