Math Reflection 1

1. In a linear relationship, the dependent variable changes as the independent variable changes. A linear relationship is when the variables go up at a steady rate. For example, if someone starts off with $100 at the beginning of the week, then is left with $80 the next and $60 the next and so on, then the money (dependent variable) is decreased at a steady rate, as the days (independent variable) is also decreasing at a steady rate. The rest of the week would look like this:
Number of Days – Money Left
0 - 100
1 - 80
2 - 60
3 - 40
4 - 20
5 - 0


2. The pattern of change for a linear relationship shows up in a table if the numbers change by decreasing or increasing at a certain rate. For example, if the table:

Miles walked-Time in minutes
2 - 20
3 - 30
4 - 40
5 - 50
The number of miles increases by 1 mile every 10 minutes, so the pattern of change would be 1 mile

The pattern of change for a linear relationship shows up in a graph is the data points are connected in a straight line. For example,

In this graph, the data points are lined up in a straight line, so this shows that the pattern of change in the graph is linear. If the data points were scattered in different places on the graph, then it would show that the points would not be lined up correctly, so there would not be a linear relationship.

The pattern of changes for a linear relationship shows in an equation if the variables are being multplied of divided. Equations are usually used for linear relationships, so if data is not linear, then there usually no equation. For example, in the equation m=20w (w=weeks) (m-money left), since the variable is multiplied, it would be a linear relationship.