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.