Stand Alone Instructional Resource By Onnie Kok

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Stand Alone Instructional ResourceByOnnie Kok
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How to solve a linear equation

• The following lessons are set up in a step by
  step layout to helping you understand and solve
  linear equations

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Lesson 1 part 1The First Step to Solving Linear
Equations

• Step 1 Recognize the variables in the question
• For any problem given to you it will always
  contain a y-intercept (b), a dependant variable
  (y) and an independent variable (X).
• Using the slope intercept form (y mxb) the
  value of y will always depend on the value of x.
  Y therefore, is called the dependant variable and
  x the independent variable.
• The y-intercept b, which is the value of y when
  X is 0, corresponds to the initial value of the
  dependent variable.
• Example At the beginning of the month, Katie
  buys a 50-pound sack of wild-bird feed. She puts
  2/3 pound in the bird feeder each morning.

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Part 2
gt In this situation, y (the dependent) would be
the number of pounds left in the sack after an x
amount of days. So, the total amount of bird feed
taken out of the sack after a certain amount of
days (X) will have an effect on how much bird
feed will be left.

After you have established what your variables
are going to be for y and x, you need to
determine their relationship to one another. One
way to know this is to ask the question, how will
they effect each other? Finally, you must
determine the rate of increase or decrease in the
problem. This represents the rate of change in
the problem and it is the slope in the equation.

• Example In the above situation the rate of
  change would be 2/3. This is your slope, m. Also,
  the situation only calls for a decrease in bird
  feed and never an increase. It should be easy to
  see that there is a constant decrease.
• Thus, your equation should look like this
  y -2/3 x 50

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Part 3

• Y -2/3 x 50
• Because of the constant decrease of bird feed
  in the sack after x days, and having a negative
  rate of change of 2/3 it would be represented as
  -2/3 x
• The number 50 in the equation (b) is the initial
  value of the dependant variable in the problem,
  the bird seed. As 50 pounds was our starting
  amount of bird seed it must therefore be used as
  shown

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Lets see what youve learned

• The following slide will be a quick quiz to test
  what you have learned thus far.
• The question will test if you can identify the
  rate of change
• It will also test your understanding of how the
  dependant and independent variable relate to one
  another

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Quick Quiz 1

• At the end of this year and every other year in
  the future, Mr. Smith will receive a 1000 bonus
  to his salary. Mr. Smiths salary had originally
  been 45 000 before the end of this
  year.
• A) Which of the below equations, best relates y
  to x in the slope intercept form?
• A Y -45000 x 1000
• B Y 1000 x 45000
• C Y 45000 x - 1000
• D Y 1000 x 45000

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Lesson 2Plotting the Points

• The next step in solving a linear equation is to
  plot certain points on a graph, using your
  equation. Using the equation in example 1
• Y -2/3 x 50, the y-intercept (b) is 50 and the
  slope is -2/3
• Step 1 Plot Y-intercept Y (pounds
  left)
• 50 -
• X (days)

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Lesson 2 part 2

• Step 2 Now, using the slope of your equation y
  -2/3 x 50, plot the next three points.
• Y (pounds left)
• 50 -
• Note
• If using a negative 40 -
• slope you must go
• down a certain 30 -
• number and then
• across to the right 20 -
• 10-
• 
  0 -
• 3 6 9
  12 15 X (days)

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Quick Quiz 2 part 1

• John has just received a new shipment of cokes.
  He plans to drink these sparingly, but
  unfortunetly he tends to drink sodas at an
  alarming rate. He received a total of 30 cokes,
  and on the first day alone he drunk 7 of them!
  Assuming he is consistent solve the following
  problems. On the graph the days multiply by
  three, cokes by 7.
• Plot the y- intercept
• Plot the point for the first day
• How many cokes will John have drunk by the third
  day?
• 
  Y
• 30 on X axis 30 on Y -axis
• 7 on Y - axis
  
  X
  

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Quick Quiz 2 part 2

• Now plot the point for the first day (
  of cokes)
• Click on the correct graph 9
• 6
• 3
• 0
• 1 2 3 ( of days)
• ( of cokes) (
  of days)
• 21
  9
• 14
  6
• 7
  3
• 0
  0
• 1 2 3 ( of days) 3
  6 9

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Quick Quiz Part 3

• How many cokes will John have drunk by the third
  day?
• A) All the cokes
• B) half the cokes
• C) exactly 2/3 of the 30 cokes
• D) 21 cokes
• E) 14 cokes

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Lesson 3 Part 1Graphing a Linear Equation

• Using the form y mx b one can easily graph
  the information given in this equation.
• If given the equation, y 6x 8, you already
  know what your slope and y-intercept is.
• When points are written, they are appear in
  brackets. Ex. (2,7) 2 is X and 7 is Y.
• Also, if given 6 as the slope, it means that
  every horizontal change of one unit to the right
  corresponds to a vertical change of six units up.

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Lesson 3 Part 2

• You have been given the equation y 3x 5 and
  the points (0,5). You are also told to graph the
  point (1,8).To graph this equation, simply use
  the slope.
• Y 3x 5
• 
  Y Connect these points with a line
• 8 - See how
  jumping 1 to right and
• 
  7 - then 3 upward to
  get the answer
• 
  6 - is using the slope?
• (0.5)
  5
• 
  4
• 
  3
• 2
• 
  1
• 
  0 -
• 
  
  
  1 2

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Exam

• Relax, this should come easy to you
• Which one of the lines below best describe the
  relationship taking place between the variables
  in the equation?
• Click on one of the ends of the correct line
• y 4x -1 ?
  6
• 
  4
• 
  2
• 
  
• -4 -2 -2 2 4
• 
  -4
• 
  -6

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Well done!

• You have successfully shown that you now know how
  to solve for a linear equation by being able to
  identify the different variables, use the slope
  in an equation, and how to graph a linear
  equation.