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Thinking with Mathematical Models

1. You can represent a relationship between variables with a table, a graph, a description in words, or an equation.

a. How can you decide whether a relationship is linear by studying the pattern in a data table?
You will be able to know it's linear because if it's consistent, the rate of change will be constant. That means the difference between two numbers will always be the same. But if the difference between the two numbers consistently change, then it's not linear.

b. How can you decide whether a relationship is linear by studying the pattern in a graph?
You will be able to know it's linear in a graph because the line will be straight. There will be no curves on it, otherwise that would be non linear. As well as if you count and know the exact number a dot is on, you will notice again that the two numbers rate of change will be constant.

c. How can you decide whether a relationship is linear by studying the words used to describe the variables?
By reading the text, you would have to look for key words or phrases. Such as ''constant rate of change''. If it says constant rate of change, it will for sure be linear because you need a consistent rate of change for it to be linear. But if it for example has the words inconsistent or different rate, it will be non linear.

d. How can you decide whether a relationship is linear by studying the equation that expresses the relationship in symbolic form?
You can find out if it's linear by looking at the equation. If you look at the leading term, which is the variable with the highest exponent, if the exponent is 1, it will be a linear equation. Also for example, if the equation is y=7, that will also be linear because it's going by a constant rate of 0.

2. What are the advantages and disadvantages of each representation in finding patterns and making predictions?
The advantages for studying the words and equation is that it's a lot faster to find since they kind of hand the information to you by telling you the rate of change. But a disadvantage of that is that it may not be as accurate, it's more risky. Although by using a data table or graph, you can get more of an accurate answer, even though it may take longer to find.
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