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Unit Content – Basic Linear Equations – Week 3

6 April 2014

Linear Functions

Linear Functions are functions that return a range based on the domain raised only to a single power. That is, the x in the function has an exponent of one. As the name implies, linear functions, when graphed, produce lines. Each point on the line satisfies the equation. That is what all the points on the line have in common, if you plug in the x of every point, and run it through the function, you will get the y-value of the point.

After reading, watching the video lectures and performing the exercises of this unit you will be able to identify lines by their defining function equation, determine a line’s equation given only two points, and use the line’s function to determine y values for any given x.

Objectives

  • Be able to identify lines based on their defining function.
  • Determine the equation of a line give only two points.
  • Use a linear function to generate any point on a line.
Reading, Videos, Discussion 2 hours
Homework 2 hours
Special Video Project 2 hours

Lecture and Reading

How Many Points Define a Line?

Part 1

Part 2

The Difference the Slope Makes

colored lines in shifting hues radiate outwards from the center origin. Various equations label the lines and certain points are plotted

Click on graph for higher resolution

The graph above is interesting for the fact that all of the functions have the same y-intercept. The difference between all of them is their slope.

The functions with a positive slope: y=4x, y=x, and y=x/4 all run upward from left to right. The lines with downward slopes in blue shades all have negative slopes: y=-x/4, y=x, and y=-4x.

Remember that the slope is a real number and represented by the ‘m’ in the slope intercept form:
y = mx + b

The graph also illustrates what all functions would look like on the Cartesian plane if all the y-intercepts where zero: All the lines would run through the origin. But the intercepts in functions are not all zero. The intercept point can be ‘translated’ up and down the y-axis, by supplying different values for b, the y-intercept.

Text Reading

Chapter 4 § 1 — 3

Homework

Three assignments:

Assignment 1

From the textbook:
Complete textbook publisher’s online homework modules 1 — 3.

Assignment 2

Last week you were introduced to the online graphing utility FooPlot. If you need a review of that revisit my introduction video for FooPlot.
This week you will use FooPlot again to graph the following equations:

  1. y = (-1, 0, 1)x + (-1, 0, -1)
  2. y = (-3, -2, -1)x + (1, 2, 3)
  3. y = (1/2, 1, 3/2)x + (2, 3, 4)
  4. y = (-1/3, -2/3, -1)x + (-4, -3, -2)

The number triplets in the parenthesis in the functions above represent random choices. For this part of the homework, you will graph the
above four functions, making a selection of your choosing for the m and b values. Plot all four functions on one graph using different colors for each line.
Post the image of your graph to the discussion board.

The second part of this FooPlot assignment is to comment on someone else’s post. Identify the graph equations by color. For example:
graph

I would comment that:
black: y = x – 1
red: y = -2x + 3
green: y = x/3 + 2
blue: y = -2x/3 -3

Please mark your posts with the “Unit 3” category.

Assignment 3

This last part of the assignment will involve some creativity on your part. You will make a short web film of an animated drawing of a function. The directions are a little complex. So give yourself
at least two hours for this assignment.

Discussion

If you have any content related questions please ask on the discussion board so others may benefit from the answers.