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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

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

Coordinate Axis

Next Slide

What was that again?

- Which axis is the red line?

X-axis

Y-axis

YOU GOT IT!

You correctly identified the y-axis. Next up

ordered pairs.

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.

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)

Example of an Ordered Pair

- The ordered pair of (2,3) is shown on the

graph here.

Name that point

- What is the correct ordered pair for this point?

(2,4)

(-4,2)

(2,-4)

Zip-pid-dee-doo-daa!!!

Nice thinking there slim. Lets keep this moving

along.

How bout ya try that one again...?

Back to the question

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)

Another question correct!

Ordered pairs is a good start, lets see where

they live.

Umm, you should rethink that answer

Back to the question

Perhaps Not?

Ordered pairs are always written in parenthesis

with the x value first and the y value second.

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.

Quadrants

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

Quality in Quadrants!!!

Surely You Want to Try Again!

Back to the question

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.

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)

Ja, dat was gouda!

No Time to Get Mad!

Back to the question

No Way Dude!!!

Back to the question

Question 2

- Which point is located in Quadrant 4?

Point A

Point B

Point C

Point D

Thats two questions correct!

A Second Chance?

Back to the question

Dr. Evil Needs Your Help!

Back to the question

Bob Calls Em Like He Sees Em

Back to the question

Query 3

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

Point A

Point B

Point C

Point D

Point E

WAY TO GO!!!

Youve answered all the questions correctly!

Lets Try That One Again

Back to the question

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

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.

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.

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

Woody Approves!

Maybe Try A Different Idea

Back to the question

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.

Nice memory

Good to see that you are not forgetting what we

just covered.

You Need A Plan For Learning This!!

Back to Ordered Pairs for you!!!

Cartesian Plane Review

- What is the correct way to describe this point?

(1,2)

X value is 1, Y value is 2

(2,1)

You dont Nemo practice!

Need Some Review?

Looks like you should take a moment and look over

Cartesian Plane information again

Back to the Cartesian Plane Review

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.

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.

Your Answer Is Nothing to Laugh At!

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.

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?

Running to Success!

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.

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.

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.

What you say?

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

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

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.

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.

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

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?

But Do You Want To Go Home?

Especially if these were your sisters?!?!

Maybe You Should Rethink That

Slope Intercept Quiz

- Which one of the following graphs shows the line

described by

?

(Click on correct graph)

Austin Toasts to You!!!

Go Back and Try Again

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

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