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 can tell if there is a constant rate of change (the variables increase constantly for both x and y). For example, if there is a table about people and dogs. There is one person with one dog, then 2 people with a total of 2 dogs, then 3 people with a total of 3 dogs. The rate of change increases by people +1 and by dogs +1 constantly (for every person there is another dog).
b. How can you decide whether a relationship is linear by studying the pattern in a graph?
You can tell when the line in the graph is completely straight and isn't curved, whether it may be a negative or positive linear equation. You can also check on the slop making sure that it is consistent (remember rise over run!)
c. How can you decide whether a relationship is linear by studying the words used to describe the variables?
Words used when describing a relationship that is linear include: constant, for every, for each, you need, etc.
d. How can you decide whether a relationship is linear by studying the equation that expresses the relationship in symbolic form?
You can look for the equation y= mx+b which will get you a straight line. Sometimes in this equation there is no be (y intercept), which means that the line would go through the origin. For example y=5x is linear as in this case b is 0, having it pass through the origin. You can tell if the line is negative or positive by looking at variable m. For example y= -x+9, this would pass through positive 9 in the y intercept and would decrease by 1.
2. What are the advantages and disadvantages of each representation in finding patterns and making predictions?
Table:
Pros-- Good for very mathematical people, who can see by the data is the line is linear and if the rate of change is constant. It's also good to compare the x and y values.
Cons-- Some people are more visual and can't really tell straight away by the data if the line is linear or not. Also there could be lots of big numbers in the data which makes the work even more time consuming and difficult.
Graph:
Pros-- It's good for visual people, you are easily able to tell if the line is straight or not. It also might be easier and quicker for some people to see if the rate of change is constant or not.
Cons-- It may be tricky to see if the line is completely straight or if it is curved slightly to the left or right. So then one would have to calculate the slope of every point to make sure that the line was straight.
Words:
Pros-- The keywords helps you understand the information quickly, because you don't have to make a table or a graph as you are able to understand if the relationship is linear or not by reading the question.
Cons-- Sometimes it's hard to tell if a relationship is linear just by looking at words if the question/problem isn't precise or clear enough or isn't on a graph or table.
Equation:
Pros-- You can plug in any number into the given equation (y=mx+b) and it gives the answer quickly with calculations.
Cons-- Sometimes you might be using big numbers taking you a long time to figure out the equation, also you might not have all the numbers needed to put into the equation, making you solve for each variable with your given data.
a) How can you decide whether a relationship is linear by studying the pattern in a data table?
You can tell if there is a constant rate of change (the variables increase constantly for both x and y). For example, if there is a table about people and dogs. There is one person with one dog, then 2 people with a total of 2 dogs, then 3 people with a total of 3 dogs. The rate of change increases by people +1 and by dogs +1 constantly (for every person there is another dog).
b. How can you decide whether a relationship is linear by studying the pattern in a graph?
You can tell when the line in the graph is completely straight and isn't curved, whether it may be a negative or positive linear equation. You can also check on the slop making sure that it is consistent (remember rise over run!)
c. How can you decide whether a relationship is linear by studying the words used to describe the variables?
Words used when describing a relationship that is linear include: constant, for every, for each, you need, etc.
d. How can you decide whether a relationship is linear by studying the equation that expresses the relationship in symbolic form?
You can look for the equation y= mx+b which will get you a straight line. Sometimes in this equation there is no be (y intercept), which means that the line would go through the origin. For example y=5x is linear as in this case b is 0, having it pass through the origin. You can tell if the line is negative or positive by looking at variable m. For example y= -x+9, this would pass through positive 9 in the y intercept and would decrease by 1.
2. What are the advantages and disadvantages of each representation in finding patterns and making predictions?
Table:
Pros-- Good for very mathematical people, who can see by the data is the line is linear and if the rate of change is constant. It's also good to compare the x and y values.
Cons-- Some people are more visual and can't really tell straight away by the data if the line is linear or not. Also there could be lots of big numbers in the data which makes the work even more time consuming and difficult.
Graph:
Pros-- It's good for visual people, you are easily able to tell if the line is straight or not. It also might be easier and quicker for some people to see if the rate of change is constant or not.
Cons-- It may be tricky to see if the line is completely straight or if it is curved slightly to the left or right. So then one would have to calculate the slope of every point to make sure that the line was straight.
Words:
Pros-- The keywords helps you understand the information quickly, because you don't have to make a table or a graph as you are able to understand if the relationship is linear or not by reading the question.
Cons-- Sometimes it's hard to tell if a relationship is linear just by looking at words if the question/problem isn't precise or clear enough or isn't on a graph or table.
Equation:
Pros-- You can plug in any number into the given equation (y=mx+b) and it gives the answer quickly with calculations.
Cons-- Sometimes you might be using big numbers taking you a long time to figure out the equation, also you might not have all the numbers needed to put into the equation, making you solve for each variable with your given data.






