Linear Functions
Natasha D. Collins
MTH/208
14 April 2011
John Rudin
Linear Functions

Question: Using the readings in Ch. 3 of the text, identify and explain at least one real-world application of algebraic concepts for one of the following areas: business, health and wellness, science, sports, and environmental sustainability. Do you think it is easier to relate this concept to one of these areas over any other? Explain why.

I think the point slope method would be good in professional sports, because you can see the process of an athlete’s career.

Question: Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain.

Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.

Question: Can one line have two slopes? Explain how or why not.

If the line is a straight line, meaning 180degrees, it can only have one slope. If it is a function (f(x) = or y=) then the line may have more than one, one, or an undefined slope. Find the first differential of the function and plug in your given x value to find the slope at any given point.

Question: What is the difference between a scatter plot and a line graph? Provide an example of each. Does one seem better than the other? In what ways is it better?
They generally refer to the same things, although some terminology may sound better with either one. For example, plot and graph, both represent data, however box plots or scatter plots or line graphs are generally referred to as such as opposed to saying box graphs, scatter graphs or line plots. The latter three sound somewhat cumbersome but technically mean the same thing.
Question: If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x- or y-intercept. Will that always be true for that situation?

This is a special case of the standard form where A = 1 and B = 0. The graph is a vertical line with x-intercept equal to a. The slope is undefined. There is no y-intercept, unless a =
0, in which case the graph of the line is the y-axis, and so every real number is a y- intercept. Question: Explain the concept of modeling. How does a model describe known data and predict future data? How do models break down? Can you think of an example?

It is use to estimate a particular number. After it is plug into a chart. Use it to make estimates about the federal inmate population

Question: What are the difference among expressions, equations, and functions? Provide examples of each.

A function always outputs a value. Suppose the function f(x) = 10x+20, what this means is that this function outputs different values for different input values of variable 'x'. For example: f(10) = 10X10+20 = 120, f(20) = 10X20+20 = 220
i.e. we substitute different values into x and get different outputs. The important point is that every function outputs a value.

Equations define the relationship between one or more variables.
Single variable equation: x2 - 10x = 0, Multi variable equation: 2x+3y = 10
An equation doesn’t output a value. We can solve the equation and find out the values of the variables. The equation would be valid only for certain values of the variables.

An expression is a finite combination of symbols that are well formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities. The use of expressions can range from simple arithmetic operations like

[pic].

References

Ask.com (2011). Cartesian equations. Retrieved from http://math.about.com
Ask.com. (2011). Expressions, equations, and functions. Retrieved from http://math.about.com.
Rockswold, G. K., & Krieger, T. A. (2009). Beginning and intermediate algebra with applications and visualization Chapter 5. (2nd Ed.). Boston, MA: Edison Wesley.