Lesson 2 - Lines:Linear Equations, Linear Systems and Linear Modeling

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Lesson 2 - LinesLinear Equations, Linear Systems
and Linear Modeling

• Functions Trig - Santowski

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(A) Linear Equations

• To write the equation of a line, we need to know
  
• (i) slope and
• (ii) a point

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(B) Linear Equations Examples

• Find the equation of the lines described below
• (1) having a slope of 3 and passing through
  (-1,-5)
• (2) through the points (-2,3) and (1,-6)
• (3) perpendicular to the line 2x y 3 0 and
  going through the point (3,8)

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(C) Graphing Lines

• Graph the lines that you determined in the last 3
  examples using (i) graphing calculator and (ii)
  graph paper
• (1) y 3x - 2
• (2) 6x 2y 12 0
• (3) 0 x 2y - 19

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(D) Linear Systems

• The term linear system implies that we have 2
  linear graphs drawn on a single set of axes
• When we solve a linear system, we try to find if
  and/or where the two lines intersect

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(E) Linear Systems Examples

• Find the intersection of the following lines
• L1 x y 5 and
• L2 2x y 1
• Using the following methods
• (1) the elimination method
• (2) the substitution method
• (3) the graphing calculator

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(E) Linear Systems Examples

• Find the intersection of the following lines
• L1 2x 3y 10 and
• L2 3x 4y 12
• Using the following methods
• (1) the elimination method
• (2) the substitution method (???)
• (3) the graphing calculator

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(F) Linear Modeling

• We can use linear equations in solving word
  problems
• Ex 1. Mario owns a construction company and
  occasionally needs to rent a small front end
  loader. ACE rentals charges 75 per day for the
  rental.
• (a) Determine the slope and the y-intercept and
  interpret their meanings.
• (b) Write the word equation and the algebraic
  expression that represents this relationship
• (c) Make a table of values
• (d) Draw the corresponding graph.

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(F) Linear Modeling

• Ex 2. A taxi fare is based on a minimum charge
  and a fixed rate for each km traveled. Find the
  equation that represents the relationship between
  the cost of the taxi and the distance traveled if

Distance (km) 20 30
Costs () 17.50 25.00
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(F) Linear Modeling

• The owner of an apartment building is going to
  buy a new air conditioner for the building. One
  brand costs 3000 to buy and 40 per month to
  operate. Another model costs 3600 to buy and
  25 per month to operate. Determine which AC is
  the owner should buy. Explain your choice.

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(F) Linear Modeling

• Wayne's Woodworking Shop makes bookcases. Wayne
  estimates that the initial cost to set up the
  assembly line for producing a bookcase is 1500
  and the cost of materials for each bookcase is
  75. The selling price of a bookcase is 125. How
  many bookcases does Wayne have to produce before
  he begins to make a profit?

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(G) Homework Policies

• All homework from this lesson will be submitted
  before 800 am on Tuesday
• ALL homework must be checked . the answers are
  in the back of the book!!!

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(G) Homework

• Section 1.3 on Linear Equations, p16,
  Q1,3,5,13,15
• Section 1. 1 for Linear Systems, p5, Q15,17
• Section 1.4 for Linear Modeling, p23, Q14,15
• Then Complete the tasks for Lesson 2 as outlined
  on the Task Sheet