math reflection 1

1. Describe how the dependent variable changes as the independent changes in a linear relationship. Give examples.

In a linear relationship, the dependent and independent variable both change according to the data. Because the dependent variable depends on the independent variable, it has to change as the independent does. For example, if Jason had $30 at the start of camp but spends $5 each day, the independent variable is the day; the dependent variable is the money because the amount of money he has depends on what day it is. So as the dependent variable decreases by 5, the independent by one, for one day. If this example was shown on a graph, the money he has left would go on the y-axis, and day on the x. The graph would show the plots below decreasing by 5 on the y-axis in a straight diagonal line. Because th eday goes across by one on the x-axis, the money must follow along. So in this example you can see how the variables change based on each other.

DAY MONEY LEFT
0 $30
1 $25
2 $20
3 $15
4 $10


2. How does the pattern of change for a linear relationship show up in a table, a graph, and an equation of the relationship?

In a table, the pattern of the numbers change by the same number, the rate. (See the table in 1, the rate is 5.^) The pattern comes from the rate in the table, because you can see that the numbers all relate to one another. In a graph, a relationship is shown by the line it makes. If it is linear, the line will be completely straight whatever way. In an equation, the pattern is shown by the number next to the variable. Example: (D=distance, t=time) d= 3t. This is linear because every "time'' is multiplied by the same number, 3. The pattern isn't really shown on the equation, but the number (or rate) allows you to see that there is a pattern.