How to Discovering Patterns: Using Graphs to Find Rules
Graphs are like picture stories of numbers.
![How to Discovering Patterns: Using Graphs to Find Rules](https://www.effortlessmath.com/wp-content/uploads/2023/11/Using-Graphs-to-Find-Rules-512x240.jpg)
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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![](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
Answers:
1. The dot will be at (2,6).
2. The dot will be at (3,2).
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