math reflection

Math Reflection

1. Linear relationships can be represented by the equation. y =mx + b. This equation is actually a form of a linear relationship. First the y in the equation (y=mx + b) represents the dependent variable. This is the variable that changes depending how the other variable increases or decreases. In a graph situation the y variable is represented by the y axis. For example in a situation the y variable would be distance. Next, the m in the equation (y=mx + b) represents the rate. This is how many times something happens per unit of time. For example: in the equation, y= 3x + 50, 3 would be the m variable. This is because 3 is the rate, no matter what number you plug in for x, it will always be multiplied by 3. Next, the x in the equation (y=mx + b) represents the dependent variable. This is the variable that increases at a steady rate. The depending variable changes depending on what the independent variable is. On a graph the independent variable is represented on the x axis. In a situation, an example of the independent variable would be time. So if the independent variable is distance and the dependent variable is time, the distance would change depending on how the time changes. Lastly, the b in the equation (y=mx + b) represents the y- intercept. The y- intercept is the point where the line in a graph crosses the y axis. For Example: in this equation, y= 3x + 50, 50 would be the y intercept. This is because 50 is the point where the line intercepts the y axis. This is how a linear relationship is represented by the equation y=mx + b.

2a. A table for a linear relationship could be used to solve a problem by using the information provided in the table. You can see the relationship between numbers in a table along with the rate, y intercept and the independent and dependent variables. You could therefore use that information to solve the problem. A graph for a linear relationship could be used to solve a problem by provided a different and some ways more clear way of the information. Some things you could see easier in a graph than a table to help you solve the problem.

b. you could use an equation for a linear relationship to solve a problem by substituting the numbers you have to solve the problem for the variables in the equation. after the numbers are substituted you follow the order of operations to solve the equation and then check your answer.