Just Graph It!

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Just Graph It!

• Jennifer Towleh

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Audience

• The first part of this tutorial is intended for
  use by 7th grade pre-algebra students who need to
  review the mechanics of plotting points.
• The second part of this StAIR can be used by all
  students as a review for chapter 13.

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Learning Objectives

• Recognize points (x,y) on the coordinate plane.
• Recognize graphed equations of the form yaxb

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Menu of Activities
Plotting points
Graphing yaxb
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Plotting Points
Learning Objective By the end of this section,
you will be able to graph and recognize points
(x,y) on the coordinate plane.
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Lets plot (4,1)
Look at the point on the diagram. Can you figure
out why this point is called (4,1)?
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Plotting (4,1)

• Point (4,1) is located where x is 4 and y is 1.

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Plotting (-4,-2)
Point (-4,-2) is located where x is -4 and y is
-2.
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(x,y) - the rule

• We find points on the plane using the coordinates
  x and y. They are written (x,y). The first
  number tells us how far it is along the x-axis
  and the second is along the y-axis.
• For example, (-4,-2) is four along the x-axis (in
  the negative direction) and two along the y-axis
  (also in the negative direction).

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Quadrants
In which quadrant would you find (-1,6)?
In which quadrant would you find (4,-2)?
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Quadrants
In which quadrant is the point (5,-4) located?

• Point (5,-4) is located in Quadrant IV.

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In which quadrant is point (-2,6)
Youll be reminded of the location of each
quadrant on the next slide.
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Which quadrant?

• The quadrant plane below will help you understand
  where ordered pairs are located and which
  variable is positive or neagtive.

(x,y) Quadrant I
(-x,y) Quadrant II
(-x,-y) Quadrant III
(x,-y) Quadrant IV
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Time to Practice
Which point represents (3,-4)?
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Quiz time
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Plotting-Question 1

• In which quadrant would you graph the point (-4,
  3)?

Quadrant I
Quadrant II
Quadrant III
Quadrant IV
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Excellent

• (-4,3) is in Quadrant II as the x-coordinate is
  negative and the y-coordinate is positive.

(-4,3)
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Try again

• Remember that for a number to be in Quadrant I
  both the x and y coordinates must be positive.

Quadrant I x positive y positive
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Try again

• In order for a number to be in Quadrant III,
  both the x and y coordinates must be negative.
  Are they both negative in this example?

Quadrant III Negative value for x Negative value
for y
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Try again

• For a number to be in Quadrant IV, you must have
  a positive value for x and a negative value for y.

Quadrant IV Positive value for x Negative value
for y
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Plotting Question 2
The point to the left represents which ordered
pair?
(-4,0)
(0,-4)
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Great work!

• It is (0,-4).
• You remembered that it is x-coordinate then
  y-coordinate.

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Try again

• This information may help you with ordered
  pairs, the x-coordinate comes first and the
  y-coordinate comes second (x,y).

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Plotting Challenge Question

• If the graph below is scaled by twos, which point
  is shown on the graph below?

(3,4)
(6,8)
(4,3)
(8,6)
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Great work!
That was a tough question. You did well!
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Try again

• Dont forget that this graph is scaled by twos.

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Try again

• Dont forget that ordered pairs are always (x,y).

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Try again

• Dont forget that ordered pairs are always (x,y)
  and that this graph is scaled by twos.

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Congratulations

• You have completed plotting!

Return to Main Menu
Continue with next section Graphing yaxb
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Graphing line yaxb

• By the end of this section, you will be able to
  recognize graphed equations of the form yaxb.
• You will be able to do this using several
  different methods.

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T-charts

• You need to determine several coordinate points
  for your line in order to graph it.
• A t-chart is one way to do this.

• The Steps
• Choose a positive and negative value for x as
  well as zero.
• Solve for y.

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Solving for y2x4
I have chosen four values for x and solved for y
below.
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The t-chart for y2x4
The numbers from the t-chart represent the
ordered pairs (1,6), (0,4), (-1,2) and
(-4,-4). We can now graph these ordered pairs
and make a line!
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How to graph y2x4
Plot the coordinate points from your t-chart.
y2x4
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Quiz time t-charts

• For y-3x4, which could not be an ordered pair
  for this equation?

(2,-2)
(0,-3)
(-1,7)
(0,4)
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Great Work!

• If x0, then y-3(0)4 which means y4 not - 3.
• You did the math correctly and read the question
  carefully.

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Try again

• Check your mathif x2, then y-3(2)4 which
  means that y-2. This ordered pair works for the
  equation y-3x4.

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Try again

• Check your mathif x0, then y-3(0)4 which
  means that y4. This ordered pair works for the
  equation y-3x4.

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Try again

• Check your mathif x-1, then y-3(-1)4 which
  means that y7. This ordered pair works for the
  equation y-3x4.

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T-chart Question 2

• Where is the mistake in the t-chart for the line
  y-2x6? Click on the arrow pointing to the
  mistake.

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Great job!

• For y-2x6. If x-3, then y-2(-3)6 so y12.
• The coordinate pair (-3,0) does not fit the given
  line as it would be (-3,12).

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Try again

• For y-2x6. If x0, then y-2(0)6 so y6.
• The coordinate pair (0,6) fits the given line.

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Try again

• For y-2x6. If x3, then y-2(3)6 so y0.
• The coordinate pair (3,0) fits the given line.

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Slope and y-intercept

• For the equation yaxb
• a is the slope of the line
• b is the y-intercept

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Slope

• The slope of a line can either be positive or
  negative.

Positive slope
Negative slope
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Slope is

• The slope of a line is rise over run. For
  example if the slope is 3 then you go up three
  and over one.
• If the slope is 2/-3 then you go up 2 and over
  three to the left (the negative direction).
• You can also think of slope as y/x in the form of
  a fraction.

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Counting out rise over run

• Below is an example of how you find the slope of
  a line using rise over run.

Start at point (0,0). You go up 3 (positive
direction along the y-axis) and go left -1
(because you are moving toward -x). The slope is
3/-1 or -3.
go up 3 go over -1
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Slope Question 1

• Is the slope of the line below positive or
  negative?

positive
negative
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Try again

• Dont forget

Positive slope
Negative slope
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Excellent work!
Yes, the slope is positive!
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Slope Question 2

• Using your skills in counting out rise over run,
  find the slope of the graph below.

2
4
-4
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Try again

• Dont forget
• The slope of a line is rise over run. For
  example, if the slope is 3 then you go up three
  and over one.

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Try again

• The direction of the line determines if it is
  positive or negative.

Positive slope
Negative slope
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Great Work!
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y-intercept

• y-intercept is simple to understand.
• It is the point at which the line crosses the
  y-axis.
• At the y-intercept, x is always zero.

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Examples of y-intercept
In this example, the y-intercept is 2 as the line
passes through the y-axis at point (0,2)
In the example above, the y-intercept is -2. All
lines that intersect below the x-axis have a
negative y-intercept.
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Determine the y-intercept
What is the y-intercept of the line above?
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Try this one
What is the y-intercept of the line above?
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y-intercept quiz
What is the y-intercept of the graph to the left?
1
2
-2
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Try again

• Dont forget that the y-intercept is where the
  line passes through the y-axis, not the x-axis.

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Try again

• Dont forget that y-intercept is either positive
  or negative depending on whether it crosses above
  () or below (-) the x-axis.

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Excellent Work
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Now

• Its time to put everything that you have learned
  about yaxb together.

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A little practice

• 1. Determine the slope which is rise/run.

2. Find the y-intercept.
3. What is the equation in the form yaxb?
3. The equation is y-3x-3.
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Quiz Question 1

• The line below represents which equation?

y2x-2
yx1
y-2x2
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Excellent work!
y2x-2
Slope is rise 2 over run 1 which is 2
y-intercept is -2
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Try again

• The y-intercept cannot be one as this line passes
  through a negative number on the y-axis.

This y-intercept is negative.
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Try again

• By looking at the graph, we know that the slope
  is positive.

This slope is positive.
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Question 2
Which of these graphs represents the line y-5x-1?
B
A
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Excellent work!
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Try again

• Dont forget
• The slope of a line is rise over run. For
  example, if the slope is -5 then you go up five
  and over one (in the negative direction).

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Congratulations you have completed yaxb
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