Math Reflection

1. In a linear relationship the dependent variable (the y axis on a graph) changes along with the independent variable (the x axis) but not at the same rate usually. If Steve is selling T-shirts at a concert for $3.00 per T-shirt you could make a table that looked like this..

X Y

1 3

2 6

3 9

4 12

5 15

6 18

7 21

8 24

9 27

10 30

As X (the independent variable) increases by one Y (the dependent variable) goes up by 3. If you put it in an equation it would be X * 3 = Y.

2. In a linear relationship the pattern of change can show up in a graph, table and an equation. In a graph you can tell if it's linear because the graph will be in a straight line and always is going at the same rate. An example of this is Steve selling his T-shirts since he has a linear equation it automatically makes him have a linear graph. You can tell if a tables linear because the numbers in the table increase or decrease in a steady rate. For example in Steve's table for every T-shirt he sells he makes $3.00 and as the table goes on Steve's money increases by a steady rate of $3.00. If you look at an equation you tell its linear because all of the numbers are compatible with each other and don't increase and decrease in the same graph or table. An example of this would be for each T-shirt Steve sells he makes $3.00 and to get how much money he makes for selling X amount of T-shirts you would do X * 3 = Y. X being the number of T-shirts bought and Y being the total money he makes off selling them.

Math Reflection

1. In a linear relationship the dependent variable changes as the independent variable changes, but they often don't change at the same rate. A linear relationship is one that changes at a constant rate and shows up as a straight line when graphed. The dependent variable is the one that depends on the other variable, and is the y that belongs on the y axis. The independent variable is the one that keeps going no matter what. It is the x that belongs on the x axis. The independent variable often goes up by 1. As the x goes up by 1, y goes up at a constant rate as well. An example of this in an equation is: y=5x or y=x+3 or y=7 (which would create a horizontal line on a graph), or y=60-5x (a decreasing linear relationship).

2. The pattern of change (or rate) in a linear relationship shows up in the table, graph, and the equation. The rate shows up in the table in the numbers. The x variable often increases by 1 and the rate will be in the numbers, which often takes some searching to find. You must look at the relationship between the y and x variable to find the pattern of change. You can tell whether the linear relationship is increasing, decreasing or not changing by observing the y or dependent variable. The pattern of change shows up in the graph on the line. As the x is steadily increasing, the y will be changing at a constant rate, and that is where the rate is to be found. In an equation, the rate is found in the numbers surrounding the y and x variables. The rate can be found in the equations above. In the equation y=5x, the rate is 5 times the independent variable. In the equation y=x+3, the rate is 1 plus a constant of 3.

Math Reflections MSA 1

1. As the independent variable increases or decreases so does the dependant variable. For example if an equation was Y=3X than every time X increases by 1 the Y increases by 3. Or if it was M=50-2W than every time W increases by 1 M decreases by 2.

2. In a graph you can tell if it’s linear if the line is straight. In table you can tell if it’s linear if the independent variable and the dependent variable both go up at a constant rate. In an equation you can tell if it’s linear if the equation has an independent variable a dependant variable and a rate.

MSA Mathematical Reflection 1

1. The dependent variable changes as the independent variable changes in a linear relationship by having the x variable ( independent variable) increase or decrease, the y variable (dependent variable) increases or decreases too. For example if a person named Kate buys two kittens every week she would have more kittens increasing by two every week that goes by.

Kate's Kittens
X Y
0 0
1 2
2 4
3 6
4 8
5 10

2. The pattern of change for a linear relationship shows up in a table, a graph, and an equation. The pattern of change for a linear relationship shows up in a table by having a repeated pattern increasing or decreasing at a constant rate. For example if the rate for Kate and her kittens is 2 kittens per week, then her table shown in number one would have the weeks(x) go up by one, and the kittens(y) go up by two's. The pattern of change for a linear relationship shows up in a graph by having the graph plots from the table go in a straight line. The line can go either way, in a straight line going up in a diagonal, in a straight line going down in a diagonal line, and or sideways in a straight line, parallel to the x axis. For example since Kate and her kittens is linear, then on a graph for every week two would go up in a diagnol by two on the y axis ( # of kittens), and would go in a straight line. The pattern of change for linear relationship shows up in an equation by having the equation work for all the numers in a constant rate. An example is also using Kates kittens by having the equation be, y=x2. These are some things to look for a linear relationship in tables, graphs, and equations.

1) In a linear relationship, the dependent variable changes as the independent variable changes. As the x variable (independent variable) increases or decreases, so does the y variable. That is a linear relationship. Example- This is a linear relationship because as x increases by 1, y increases by 2. They both increase at a steady rate, which makes it linear.
x y
0 0
1 2
2 4
3 6
4 8
5 10

2) The pattern of change for a linear relationship shows up in a table, a graph, and an equation.
Table- The pattern shows up when y goes up or down at a constant rate while x does also.
Graph- The pattern shows up when the line is straight.
Equation- The pattern shows up in an equation when the equation works for all numbers and they come out in a constant rate.

MSA Math Reflections 1

1. How the dependent variable in a linear relationship changes depends on how the independent variable changes. For example, if in the bike-athon, Mr. Murphy's class generated $200.00 to give to charity. Each week they donate $20.00 to the local Children's hospital. The independent variable is weeks and the dependent variable is the money left in the account. As the weeks increase by one, $20 is deducted from the class account. Another example of this is Joey works for his neighbor. For every hour that he works, he gets paid $10.75. The independent variable is hours while the dependent variable is how much Joey gets paid. As the hours increase by one, Joey earns $10.75 more.

2. The pattern of change in a linear relationship shows up as:

Graph, A straight line going either up or down.

Table, Increases or decreases with the same rate as time moves on.

Equation, A steady rate, if the same amount is added or taken away as time moves on.

1. The dependant variable changes as the independent variable changes in a linear relationship, because if the independent variable increases, so does the dependant variable, and if the independent variable decreases, so does the dependant variable. For example, in problem 4 on page 13, as the time increases by 1 hour, the distance increases by 6.5 miles.

2. The pattern of change for linear relationship shows up in a table, because if there is a steady increase in the numbers, then there will be a linear relationship, but if the numbers have no pattern, there will not be a linear relationship. The pattern of change shows up in a graph, because if there is a straight line on the graph, that shows a linear relationship between the numbers, and if the data in the graph doesn't make a straight line, then there will not be a linear relationship. The pattern of change for linear relationships show up in an equation, because if the equation does not work for all numbers, then there will not be a linear relationship. If the equation woks for every number that you try and it makes a linear relationship, then the equation and data are linear.

Math Reflection

1. The dependent variable changes as the independent variable changes in a linear relationship. If the independent variable increases by 1, and the dependent increases by 5 each time, it is changing in a linear relationship. It is changing in a linear relationship because it is going up by 5 each time, and it doesn't change. If you sketched a graph the line would come out straight because it is evenly going up by 5 each everytime the independent variable increases by 1. For example, if the independent variable increases by 2 each time, and the dependent variable is increasing by 4 each time, it is changing in a linear relationship.

2. The pattern of change for a linear relationship shows up in a table, graph, and an equation of the relationship. It shows up in a table, if X shows up as 2,4,6,8,10 and Y shows up as 10,20,30,40,50, then it is linear because it is increasing by the same number (10) every time it increases by 2. In a graph a pattern of change in a linear relationship would show up by showing a straight line on the graph. For example, if X was increasing by 5 on the X axis, and Y was increasing by 20 on the Y axis, then a straight line would come out when you graphed it. The pattern of change for a linear relationship shows up in a equation of the relationship because the equation stays the same with the same numbers. For example, if X was 1 and Y was 5 the equation would stay as 5y=x.

MSA Math Reflection 1

1. As the independent variable changes, the dependent variable does too. It either increases, decreases, or stays the same. For example, if the independent variable is weeks and the dependent variable is money, the dependent variable will increase if you receive money, decrease if you spend it, or stay the same if you don't spend or get any.
2. You can see patterns and linear relationships in tables, graphs, and equations. In a table, you can see the relationship if the data increases at a steady rate. For example, if money increases by $5 every week. In a graph, you can see the relationship if there is a straight line of data points, increasing, decreasing, or staying the same at a constant rate. In an equation, there must be a number that can be multiplied, divided, added, or subtracted by the independent variable to equal the dependent variable. For example; m=5w. M= amount of money W=weeks. There are many ways to figure out if there is a linear relationship of data.

Math reflection

1. If the graph is linear than the dependent variable goes down at a steady rate. So as the independent variable goes up or down the dependent variable will go up or down by the same number every time. For example on p. 11 problem 1.4 part B has a graph that is linear because the dependent variable goes down by 10 every time the independent goes up by 1.

2. Graph: If the line is a straight line than it is a linear relationship. Table: If it is miles per hour the miles should go up or down at a steady rate as the hours go up than it is a linear relationship. Equation: If the equation is like y=x with an exponent over the x it is not linear but if the equation is like y=2x+73 it is linear. Or even if it is like y=53 it is linear.