Mathematical+Reflections,+p+34+10-11

[|Khan Academy]

May 6, 2011 AS

Big Idea: Many real world situations can be modeled and predicted using mathematics Essential Question: What is the relationship between a table, a graph and an equation?

Notes from Class: · The coefficient of x is always the rate · Slope: y = mx + b  · Slope (m) is a number that tells us how steep a line is. · Slope = m = rise/run = change in y/change in x  · Y -intercept: y = mx + b

On a table, you can tell whether the relationship is linear by finding the slope (or rate of change). Basically, if all of the numbers increase by the same number, it is linear. On an equation, you can tell whether the relationship is linear if the constant, m (the slope) is present and if the constant b (y-intercept) is present.
 * 1. How can you decide whether a relationship is linear by looking at its table or its equation?**

In the table, if the data went up by the same number, the relationship was linear. The number that it goes up by is known as the rate. In the graph, if the coordinates formed a straight line, the relationship was linear. The number between each coordinate is the rate. In the equations, the coefficient of x (number before x) is always the rate.
 * 2. In the situations you explored, how did the rate – such as the meters per second a students walks or the dollars per mile a sponsor pledges – show up in the table, the graph, and the equation of a linear relationship?**

For graphs, you can compare the way the lines look. For tables, you should look at the starting number and the end number and look at the differences. For equations, you should compare the numbers before and after x.
 * 3. How can you compare the rates for two linear relationships by looking at their graphs? Their tables? Their equations?**

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?** I might use a graph to answer a linear relationship if I want to see how steep a line is. I might use a table if I want to compare the rates of the linear relationship. I might use an equation if I want to work out the y-intercept.

During this investigation, we dealt a lot with comparing the different uses of graphs, tables, and equations – especially when we’re dealing with linear relationships. I find them really confusing and I’m scared I’m not going to do very well on the check-up. But the ACE was good practice for me and I hope the next few investigations clear up some of my questions about slopes and y-intercepts because I’m still pretty uncomfortable with them.
 * Summary**