M8+ Blog TWMM Unit 1 reflection

M8+ Blog TWMM Unit 1 Reflection questions:

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 decide how a relationship is linear on a data table by finding how much each step increases by. If they all increase by the same amount than when put on a graph the line will be linear or straight. If one or more do not increase by the same amount than the line is not linear. 

B. How can you decide whether a relationship is linear by studying the pattern in the graph?

You can decide how a relationship is linear on a graph by drawing a line from each marker on the graph, connecting the markers. Then by studying the line we can tell if it’s linear. If the line continues forward in a strait line it is linear, if it does not than it is not linear.

C. How can you decide whether a relationship is linear by studying the words used to describe variables?

You can decide how a relationship is linear by using the words used to describe variables. If the words used to describe the variables are that they form a constant slope and increases by the same amount every time then it is a linear or a straight line. If they only use the word slope and they say that it depends on what number it is to tell what it increases by then it is not a linear or straight line.

D. How can you decide whether a relationship is linear by studying the equation that expresses the relationship in symbolic form?

You can decide how a relationship is linear by seeing if the equation fits the symbolic form. The symbolic form for a line is y=mx+b, If your equation fits the symbolic form than you know its linear or a straight line. If it does not fit the symbolic form than you know it is not linear or a straight line. 

2. What are the advantages and disadvantages of each representation in finding  patterns and making predictions?

A. 

Advantage: You can fill in the gaps between the tables, making it easier to see if it increases by the same amount.

Disadvantage: If you slip up on a simple addition problem for at least one of them it can change your results from linear or straight to not linear or straight. 

B. 

Advantage: You can physically see the straight or linear line.

Disadvantage: If you put the marker off by a little bit it can be hard to tell if the whole line is linear or straight.

C. 

Advantage: It is quick and easy to look for the words slope, constant, and increase by same value every time.

Disadvantage: If you get to quick and skip over some words, chances are you might skip over one that is crucial to determining if it is linear or not.

D.

Advantage: You already know the symbolic form that you need to apply your equation to so that makes it quick and efficient.

Disadvantage: If you have never worked with the symbolic form for a line than you may get your answer wrong.