Graphing Lines

1
Graphing Lines

• This is an interactive learning module that
  will help you with the task of mastering the
  basics of graphing. In this module you will
  learn how to
• Describe a point on a Cartesian plane.
• Identify the format of the slope-intercept form.

Next Slide
2
Coordinate Axis

• A line is a series of points that can be
  described in 2 dimensions. Each point can be
  located on a grid, called a Cartesian plane.
• The x-axis is in the horizontal direction.
• The y-axis is in the vertical direction.

Next Slide
3
Coordinate Axis
Next Slide
4
What was that again?

• Which axis is the red line?

X-axis
Y-axis
5
YOU GOT IT!
You correctly identified the y-axis. Next up
ordered pairs.
6
Not Quite!!!
You did identify an axis, but the x-axis is
horizontal. The y-axis is the one in red and it
runs vertically.
7
Ordered Pairs

• Each point of a line is described by its location
  on the horizontal and vertical axis. This is
  called an ordered pair.
• Ordered pairs are always written in the following
  format
• (x-axis location, y-axis location)

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Example of an Ordered Pair

• The ordered pair of (2,3) is shown on the
  graph here.

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Name that point

• What is the correct ordered pair for this point?

(2,4)
(-4,2)
(2,-4)
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Zip-pid-dee-doo-daa!!!
Nice thinking there slim. Lets keep this moving
along.
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How bout ya try that one again...?
Back to the question
12
Another review

• How are ordered pairs always written?

(x value, z value, y value)
(y value, x value)
I dont remember, take me back to show me how
(x value, y value)
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Another question correct!
Ordered pairs is a good start, lets see where
they live.
14
Umm, you should rethink that answer
Back to the question
15
Perhaps Not?
Ordered pairs are always written in parenthesis
with the x value first and the y value second.
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Quadrants

• Points on a Cartesian plane can have both
  positive and negative x values as well as both
  positive and negative y values.
• This means that the 4 combinations of coordinates
  can be placed in one of four places on a
  Cartesian plane.
• Each of these 4 places is called a quadrant.

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Quadrants
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Where am I?

• If I were standing on a spot that was
  described by (-4, 2), what quadrant would I be
  located in?

Quadrant I
Quadrant II
Quadrant IV
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Quality in Quadrants!!!
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Surely You Want to Try Again!
Back to the question
21
Quiz on Ordered Pairs

• Time to give that brain of yours a quick quiz
  on what we have looked at covering ordered pairs.
  You have to get the three questions correct
  before you can move on. Lets see what you know.

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Question Numero Uno

• How do you describe a point?

An ordered pair that has both x and y values
Drawing it on a map
Really carefully
Write it down in the form of (y value, x value)
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Ja, dat was gouda!
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No Time to Get Mad!
Back to the question
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No Way Dude!!!
Back to the question
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Question 2

• Which point is located in Quadrant 4?

Point A
Point B
Point C
Point D
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Thats two questions correct!
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A Second Chance?
Back to the question
29
Dr. Evil Needs Your Help!
Back to the question
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Bob Calls Em Like He Sees Em
Back to the question
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Query 3

• What point be me? I am standing in Quadrant 3

Point A
Point B
Point C
Point D
Point E
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WAY TO GO!!!
Youve answered all the questions correctly!
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Lets Try That One Again
Back to the question
34
Slope Intercept Format

• Lines are described in Algebra in many ways. One
  of the ways that a line can be described is in
  slope intercept form.
• Slope intercept form puts the equation of a line
  into a format that stresses 2 keys parts
• The slope of the line
• Where the line intersects the y-axis

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Slope

• All lines are not the same and are describe in
  different ways. The major way in which lines are
  different is the slope of the line.
• The slope of a line is basically how steep the
  line is. The higher the number, the steeper it
  is.

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Slope

• The common way to describe the slope of a line is
  to look at it as

or how much you move up and down over how much
you move left or right.
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What about this one?

• Can you identify the slope of this line?

Yup, its 4
Easy enough, its 1/2
No problem, its 2/1
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Woody Approves!
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Maybe Try A Different Idea
Back to the question
40
Id like to place an order

• I would like one ordered pair please. And no,
  I do not want to supersize my ordered pair.
• If I were to ask for one of these, what would I
  be asking for?

A list of x and y values that makes up all the
points of a line.
A description of a point that has its x value
first and then its y value.
Not quite sure, would you be nice enough to show
me that info again?
Two numbers in parenthesis that are added
together.
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Nice memory
Good to see that you are not forgetting what we
just covered.
42
You Need A Plan For Learning This!!
Back to Ordered Pairs for you!!!
43
Cartesian Plane Review

• What is the correct way to describe this point?

(1,2)
X value is 1, Y value is 2
(2,1)
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You dont Nemo practice!
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Need Some Review?
Looks like you should take a moment and look over
Cartesian Plane information again
Back to the Cartesian Plane Review
46
Intercepting

• Where a line crosses the y-axis on a Cartesian
  plane is known as the y-intercept.
• In this example, the point (0,2) is the
  y-intercept.

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Name that intercept

• Using the graph shown, what is the y-intercept
  of the line?

Why dont you ask hard questions? I know the
intercept is 2.
Cmon Mr.C, the answer is easy to see as the
y-intercept is -3.
I dont care what the other answers do, I say its
-2.
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Your Answer Is Nothing to Laugh At!
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That Wasnt The Correct Answer
The y-intercept of a line is where the line
crosses the vertical y-axis. In this case, the
y-intercept was -2.
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Slope?

• Using the same line as you just saw, what is
  the slope of the line?

Slope is easy to do, its as easy as -3 over 2.
I found it to be 2 over -3.
I need some review, can you show me what to do?
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Running to Success!
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Sliding With Slope?
Remember that slope is determined by the rise
over the run. Count the number of squares the
line goes up/down and then divide that by how
much the line goes left/right.
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Slope Intercept Form

• To combine the concepts of slope and y-intercept
  together, we can describe the line in the slope
  intercept format.
• The slope intercept form of a line makes it easy
  to identify the parts that are the most
  frequently used to describe the line.

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Slope Intercept Form

• The slope intercept of a line is written as
• Where m is the slope of the line and b is the
  y-intercept.

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What you say?

• Slope is the steepness of the line.
• Y-intercept is where the line crosses the y-axis.
• Slope Intercept form is

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Put that brain to work

• Time to stretch the noggin and think. I know
  that its not fair for me to ask that of you but
  you have to come expect that from me get over
  it. ?
• If the slope of a line has a negative rise and a
  positive run, what type of number will the slope
  be?

Negative
Positive
57
Didnt You Mean To Say Negative?
Remember when a positive and negative number are
multiplied or divided that the result is a
negative number. Two positive numbers or two
negative numbers will produce a positive answer
when they are multiplied or divided.
58
Way to extrapolate!!!

• The slope of a line can be either positive or
  negative.
• A positive slope can have either both positive
  rise and run or both negative rise and run (two
  negatives make a positive).
• A negative slope will have either a negative rise
  or a negative run but not both.

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Visualize that please

• Hey Mr.C, I dont understand what this
  positive and negative slope stuff is. Can you
  show me?
• Sure, how bout those graphs, can ya see what I
  mean now?

Positive slope
Negative slope
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A walk home from school

• If you are at the top of this hill and your house
  is at the bottom, what is the slope of the path
  you have to take to get home?

Positive
Negative
I cant remember, can you show me again?
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But Do You Want To Go Home?
Especially if these were your sisters?!?!
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Maybe You Should Rethink That
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Slope Intercept Quiz

• Which one of the following graphs shows the line
  described by

?
(Click on correct graph)
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Austin Toasts to You!!!
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Go Back and Try Again
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CONGRATS!!!
You have made it through the module on the basics
of graphing. Now go out there and do something
with it like graph how much you have grown over
the course of this year. Be sure to put it in
the proper slope-intercept format.
Certificate Of Achievement
End Module