Mathematical+Reflections,+p+34

24-05-09 Eva v. V. Mathematical Reflections Investigation 2

** Big Idea: ** Many real world situations can be modeled and predicted using mathematics. A relationship is linear when the data in the table follows a constant pattern; so if the numbers increase by 2 (dollars) for each 1 (mile), the relationship is linear, but if for each 1 (mile) you increase by 10, then 2, then 7 (dollars) there is no linear relationship, because there is no constant pattern. You can know whether a relationship is linear by looking at its equation because there will only be a coefficient, no +6 or -8.
 * Essential Question: ** What is the relationship between a graph, a table and an equation?
 * 1. How can you decide whether a relationship is linear by looking at its table or its equation? **

In the table it showed up as numbers that increased by the same amount each time; a constant pattern. On the graph it showed up as an increasing line that kept the same slope. In the equation the rate of a linear relationship showed up as only a coefficient, no adding or subtracting.
 * 2. In the situations you explored, how did the rate – such as the metres per second a student walks or the dollars per mile a sponsor pledges – show up in the table, the graph, and the equation of a linear relationship? **

Constant rate shown in graph:

 You can compare the steepness of the line on their graphs, as the steeper line will have a greater rate of change. By looking at their tables you can compare the amount by which the numbers increase each time, the patterns; and for the equations you can compare the coefficients; the equation with a larger coefficient will have a greater rate of change.
 * 3. How can you compare the rates for two linear relationships by looking at their graphs? Their tables? Their equations? **

You might use a graph when you want to see how greatly something declined or decreased, and whether it declined/decreased fast or slowly compared to another linear relationship. You might use a table when you want to know what the rate of change is, and you might use an equation when you want to figure out data that you would otherwise have to extend you graph or table for, or when you want to compare the rate of change between 2 linear relationships.
 * 4. When might you use a graph to answer a question about a linear relationship? When might you use a table? When might you use an equation? **


 * Summary:** In this investigation, we learnt about linear relationships and how to use, recognise and compare them, using tables, graphs and equations. We also learnt about the effect that changing the rate has on tables, graphs and equations.