Mike May College Algebra

Mike May, Feb 4, 2017

A set of applets for College Algebra - Under Development

Table of Contents

  1. Chapter 2 Graphs of lines
    1. Lines from 2 points
    2. Writing Equations of Parallel and Perpendicular Lines
    3. Writing the Equation of a Line (I-VA)
  2. Chapter 2-2a Writing Linear Equations
    1. Writing the Equation of a Line (I-VA)
    2. Writing the Equation of a Line Given a Slope & Point (V1)
    3. Writing Linear Equations Given Slope & Point (V2)
    4. Writing Linear Equations Given 2 Points (y-int = integer)
    5. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    6. Writing the Equation of a Line (I-VA)
    7. Writing Equations of Parallel and Perpendicular Lines
    8. Standard Form to Slope-Intercept Form (Rewriting Linear Equations)
    9. Writing the Equation of a Line Given Both Intercepts
  3. Chapter 2-2b Graphing Linear Equations
    1. Blueprint Equation of a Line (I)
    2. Blueprint Equation of a Line (II)
    3. Equation of a Line: Dynamic Illustrator
    4. Graphing Linear Equations: Question Generator (V2)
  4. Chapter 2-3 Graphing Circles
    1. Graph the Circle
    2. Circle and Completing the square demo
    3. Complete the square -- quadratics
  5. Solving Linear Systems Graphically
    1. Is P(x, y) a Solution?
    2. Solving Linear Systems Graphically
    3. Modeling Linear Growth (and Systems Introduction)
    4. Solving Linear Systems by Graphing: Quiz (V1)
    5. Solving Linear Systems by Graphing: REVAMPED
  6. Solving Linear Systems Algebraically
    1. Solving Linear Systems Algebraically: Quiz (V1)
    2. Solving Linear Systems Algebraically: Quiz (V2)
    3. Solving Linear Systems Algebraically: Quiz (V3)
  7. Inequalities with 2 Variables
    1. Linear Inequalities of 2 Variables: Illustrator
    2. Graphing Linear Inequalities with 2 Variables (Quiz)
    3. Inequalities in Standard Form (Illustrator)
    4. Graphing Linear Inequalities Written in Standard Form (Quiz)
    5. Solutions to Linear Inequalities
  8. Quadratic Functions
    1. Family of parabolas

1.

Chapter 2 Graphs of lines

  • 1. Lines from 2 points
  • 2. Writing Equations of Parallel and Perpendicular Lines
  • 3. Writing the Equation of a Line (I-VA)

1.1.

Lines from 2 points

This worksheet looks at lines, starting with two points and then converts the information into the various formats we have for lines.[br]The two points are P and Q and they can be moved by dragging.[br][br]The 2 point version of the line, or L2pt(x) is obtained by plugging in the coordinates of P and Q.[br][br]For the point slope form, or LPtSlp(x) we first need to computer the slope by finding the change in y and the change in x between the points.[br][br]For the slope-intercept form, or LSlpInt(x), we need to compute the intercept b.[br][br]For the general form of the line or LGen(x) I need to show that the change in x and y, times the values of y and x equal the result form a given point.
– Mike May

1.2.

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1.3.

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2.

Chapter 2-2a Writing Linear Equations

Material from TIm Brzezinski on Writing Linear Equations

  • 1. Writing the Equation of a Line (I-VA)
  • 2. Writing the Equation of a Line Given a Slope & Point (V1)
  • 3. Writing Linear Equations Given Slope & Point (V2)
  • 4. Writing Linear Equations Given 2 Points (y-int = integer)
  • 5. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 6. Writing the Equation of a Line (I-VA)
  • 7. Writing Equations of Parallel and Perpendicular Lines
  • 8. Standard Form to Slope-Intercept Form (Rewriting Linear Equations)
  • 9. Writing the Equation of a Line Given Both Intercepts

2.1.

– Tim Brzezinski

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Chapter 2-2b Graphing Linear Equations

Material from TIm Brzezinski

  • 1. Blueprint Equation of a Line (I)
  • 2. Blueprint Equation of a Line (II)
  • 3. Equation of a Line: Dynamic Illustrator
  • 4. Graphing Linear Equations: Question Generator (V2)

3.1.

Blueprint Equation of a Line (I)

[color=#000000]This applet accompanies the [/color][i][color=#0000ff][b]Blueprint Equation of a Line[/b] [/color][/i][i][color=#0000ff]lesson activity[/color][/i][color=#000000] given to you in class. [br]Please use this applet to help you complete this activity.[br]If, at any time, you need to reference the [/color][i][color=#0000ff]Slope: Intuitive Introduction [/color][/i][color=#000000]applet, it can be found [/color][url=https://tube.geogebra.org/m/Xutr9rPj]here[/url][color=#000000]. [br][br][/color][color=#000000][b]Teachers:[/b] [/color][color=#cc0000][b]A pdf copy of this[/b] [/color][color=#0000ff][b]lesson activity [/b][/color][color=#cc0000][b]can be found below this applet.[/b][/color]
Blueprint Equation of a Nonvertical Line (Investigation)
– Tim Brzezinski

3.2.

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3.3.

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3.4.

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4.

Chapter 2-3 Graphing Circles

  • 1. Graph the Circle
  • 2. Circle and Completing the square demo
  • 3. Complete the square -- quadratics

4.1.

Graph the Circle

Drag points A and B so the circle matches the given target equation.
– Steve Phelps

4.2.

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4.3.

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5.

Solving Linear Systems Graphically

  • 1. Is P(x, y) a Solution?
  • 2. Solving Linear Systems Graphically
  • 3. Modeling Linear Growth (and Systems Introduction)
  • 4. Solving Linear Systems by Graphing: Quiz (V1)
  • 5. Solving Linear Systems by Graphing: REVAMPED

5.1.

Is P(x, y) a Solution?

Drag the point to various positions (both ON and OFF the line). Pay attention to what you see here. Then, answer the questions that follow.
If a point [math]\left(x,y\right)[/math] LIES on a line with a given equation, what can we conclude?
If a point [math]\left(x,y\right)[/math] DOES NOT LIE on a line with a given equation, what can we conclude?
If we wanted to see whether [math]\left(4,-3\right)[/math] was a solution to the equation [math]3x-5y=27[/math], what would we need to do first?
Is [math]\left(4,-3\right)[/math] a solution to the equation [math]3x-5y=27[/math]?
If we wanted to see whether [math]\left(-3,4\right)[/math] was a solution to the equation [math]3x-5y=-30[/math], what would we need to do first?
Is [math]\left(-3,4\right)[/math] a solution to the equation [math]3x-5y=-30[/math]?
– Tim Brzezinski

5.2.

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5.3.

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5.4.

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5.5.

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6.

Solving Linear Systems Algebraically

  • 1. Solving Linear Systems Algebraically: Quiz (V1)
  • 2. Solving Linear Systems Algebraically: Quiz (V2)
  • 3. Solving Linear Systems Algebraically: Quiz (V3)

6.1.

Solving Linear Systems Algebraically: Quiz (V1)

[b]Directions:[/b][br][br]On a separate sheet of paper, solve the system of linear equations shown in the upper right hand corner of the applet. Once you obtain your solution, move the BIG WHITE POINT (shown in the coordinate plane on the left) to the location of the solution of this system. [br][br][color=#ff7700][b]If you solve this system correctly, the applet will automatically notify you. [/b][/color][br][br][color=#0000ff][i]Generate as many practice problems as you need in order to master this concept! [/i][/color]
– Tim Brzezinski

6.2.

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6.3.

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7.

Inequalities with 2 Variables

  • 1. Linear Inequalities of 2 Variables: Illustrator
  • 2. Graphing Linear Inequalities with 2 Variables (Quiz)
  • 3. Inequalities in Standard Form (Illustrator)
  • 4. Graphing Linear Inequalities Written in Standard Form (Quiz)
  • 5. Solutions to Linear Inequalities

7.1.

Linear Inequalities of 2 Variables: Illustrator

Suppose we graph the inequality [math]y>\frac{1}{2}x+2[/math]. This graph can be described as
Suppose we graph the inequality [math]y<\frac{1}{2}x+2[/math]. This graph can be described as
Suppose we graph the inequality [math]y\le\frac{1}{2}x+2[/math]. This graph can be described as
Suppose we graph the inequality [math]y\ge\frac{1}{2}x+2[/math]. This graph can be described as
– Tim Brzezinski

7.2.

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7.3.

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7.4.

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7.5.

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8.

Quadratic Functions

  • 1. Family of parabolas

8.1.

Family of parabolas

This applet lets you look at the graphs of parabolas in vertex form.
– Mike May

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