MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.1.htm © 2025   A2, Agnes Azzolino Distance Formula, Midpoint Formula, Circles, Solving equations graphically. Text 2.1,2.2, PG. 72, 87

Welcome to Precalc! This is a typical "fly through day" -- too much review material to get all students "up to precalc speed" Hi,     I consider today's work super easy for some and a real challenge for others. If you become overwhelmed, request an office hour as soon as possible using the pink box listed just below.     Contact me through the pink box on www.mathnstuff.com/math/math.htm if you need me or with the phone number on your class CANVAS home page.     Hang in there. Welcome to college level math.     Stay safe, A2

0 - not in the book - math symbols
2.1 - The Rectangular Coordinate Systems and Graphs, pg. 74, Learning Objectives
	* Plot ordered pairs in a Cartesian coordinate system. Graph equations by plotting points.
	* Graph equations with a graphing utility. Find x-intercepts and y-intercepts.
	* Use the distance formula.
	* Use the midpoint formula.
2.2 - Linear Equations in One Variable, pg.  87, Learning Objectives
	* Solve equations in one variable algebraically.
	* Solve a rational equation.
	* Find a linear equation.
	* Given the equations of two lines, determine whether their graphs are parallel or perpendicular.
	* Write the equation of a line parallel or perpendicular to a given line.

Day #, Chapter.Section    Text Page & Content/Topic

 

0 math symbols: their meaning, how to write them, how to say them 2.1, 2.2

2.1 The Rectangular Coordinate Systems and Graphs, pg. 74

      coord sys @ 74, plot @ 76, TI graph @ 78, intercepts @ 79, distance @ 80, midpoint @ 82, circle @ 83, exercises @ 84

• plot, graph
  Cartesian -- definition and analytic history web page
  graphing "What's A Graph?"
• compute
  distance.gsp   -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
  
  
• Distance Formula, Midpoint Formula, Circles, Solving equations graphically

• GraphGivenCircle   -- Graph a circle by graphing + and - functions defined by parameters.
      * Also states equation of circle.
• Distance computation page in One-, Two-, Three-, and N-Space
• Functions and Operations Computation Page - midpoint, slope, distance, ...
• argument
• radicand
  distance   -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance

  circleTangent   -- writes the tangent to a given circle

  GraphGivenCircle   -- Graph a circle by graphing + and - functions defined by parameters.
      * Also states equation of circle.

  circleFormula   -- writes the formula for the depicted circle

  circles, distance formula, tangents, normals
  circle.tangent.normal.gsp
      1 drag center & radius 2 create equation
      2 enter h, k, r
      3 input coord, m=, line=, perp=
      4 slide, write tangent & normal
  just circleFormula   -- writes the formula for the depicted circle
  just circleTangent   -- writes the tangent to a given circle

2.2   Linear Equations in One Variable, pg. 87

      lines @ 88, solve linear equ. @ 88, solve rational (fraction equation

@ 89, Solving Rational Equations with a Binomial in the Denominator @ 91,

      slope @ 83, write equ of lines @ 94, parallel, perpendicular @ 96, exercises @ 100

• LINES -- Notes, Discussion, Activities
• Line Vocabulary
• line gsp   -- slide points A and B and generate equation of the line in 4 forms.
• linear.xls for: graphs, slope
• SLOPE SONG
• "Worn for Work -- Solve Systems of Linear Equations" Connect the Dots
• Who Has? Lines Game Cards
• trace   -- creates point defined by an x-intercept and a calculated value for y of point
  then traces the path of the point controlled by the x-intercept
• Ed's Line Project Handouts: 1a, 2a
• 
  
  LINES -- Notes, Discussion, Activities
  Line Vocabulary
  line.gsp   -- slide points A and B and generate equation of the line in 4 forms.
  line.gsp   -- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
  -- slide points A and B and generate equation of the line in 4 forms.
  -- computes slopes and writes lines by sliding and by parameters
      1 - drag segment endpoints to compute midpoint and distance
      2 - show how the distance formula computes
      3 - find a perpendicular w/input coordinates
      4 - find parallel w/input coordinates
  linear.xls for: graphs, slope
  SLOPE SONG .htm
  solve equ w/solver -- find x-intercepts
  solve graphically
  equations of lines .htm
  Graph papers
  Three Regular Planes Graph Paper      
  Three Trig Planes Graph Paper Precalc TEXTBOOK Info
  Precalc DownLoad or View the Text