It is time to review GRAPHING LINEAR EQUATIONS

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It is time to reviewGRAPHING LINEAR EQUATIONS

• Lovingly created by your math teacher
• Ms. C. Chaboyer

Press here
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What do I need?
Be sure that you have a
a
and some
Press here
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How do I use this StAIR?
1) READ the information on the screen
2) THINK about the information
3) ANSWER the questions
4) TAKE notes on important information
5) PRACTICE graphing the equations on your paper
Press the blue button to move to the next slide
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Yeah butwhat will I learn?

• To identify slope and y-intercept when given an
  equation in slope-intercept form
• 2) To graph a linear equation when given an
  equation in slope-intercept form
• 3) To convert a linear equation from standard
  form to slope-intercept form
• 4) To graph a linear equation when given the
  equation in standard form.

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Slope-intercept form of a line
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What is the slope-intercept form?
where m is the slope b is the y-intercept
Think of the form as y slope x y-intercept
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Need a Reminder about Slope and Y-Intercept?
There is a quiz for you to try or a short
tutorial for you to use if you need a reminder.
Yes
NO
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What is the slope of a line?

• You can think of slope of a measure of the
  steepness of a line

y
y
C
B
x
x
A
D
positive slope
negative slope
From A to B Rise is Run is
From C to D Rise is - Run is
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1. Slope is

• Rise is the change in the vertical direction
  (y-direction)
• Run is the change in the horizontal direction
  (x-direction)

If the slope is then the line rises 2 and
runs 3 or you can think that the line rises -2
and runs -3
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2. Slope is

• m in
• Therefore the slope of

-1
2
is
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Test your slope knowledge!

• Identify the slope of the line described by

-2
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Wow, too bad.
Look to the right and you will see the
information again. Notice that the slope is
coefficient (number in front) of x.
Return to question
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CONGRATULATIONS!!!
Way to go!
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What is the y-intercept?

• The red point on
• the graph IS the
• y-intercept.

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1. y-intercept is

• The point where the graph crosses the y-axis
• The coordinates of the y-intercept are always
  (0,y-value)

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2. y-intercept is

• b in the equation
• Therefore the y-intercept of
• is 2

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A quick review of y-intercept

• What is the y-intercept of the line shown?

0
5
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Yikes! Too bad.
Ask yourself, Where does the line cross the
y-axis?
Return to question
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You got it right! Excellent!
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Quiz

• Soyou think that you know all about slope and
  y-intercept? Well, prove it! Take the 3 question
  quiz!

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Question 1
, which statement is true?
Given the equation,
Slope is 3
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Dont get frazzled.
Calm down and go back to the information. Relax,
think and try it again!
Helpful hint
We know that the slope-intercept form is
y slope x y-intercept
y 5x 3
Sofor
Return to question
slope 5 y-intercept 3
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CONGRATULATIONS!!!
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Question 2

• What is the slope of the line that is expressed
  by

18
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Wow, too bad.

• Lets try that problem again, shall we?

Remember m is slope
Return to question
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Excellent work!
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Question 3

• What is the y-intercept of the graph shown?

2
3
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Oops! Not quite right.
y-intercept
Return to question
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Hallelujah!!! You got it right!
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Graphing from ymxb
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Steps to follow
Find the y-intercept from the equation. Put the
y-intercept on the graph.
Find the slope from the equation. Identify the
rise and the run from the slope.
From the y-intercept, rise 3 and run 4. Plot
your second point.
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Lets try it together!

• Get out your graph paper, pencil and ruler
• We are going to try to graph a line together
• Ready?
• Lets GO!

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Equation of the line
Ask yourself 1) What is the y-intercept? b 2)
What is the slope? m 3) What is the rise?
numerator of slope 4) What is the run?
denominator of slope
3
-3
2
Write down your answers, you will need them for
the next step.
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Step 1 Plot the y-intercept.
Rise -3 Run 2
Step 2 Rise -3 and then run 2. Plot your second
point.
Step 3 Connect the points with a line.
We will practice together one more time.
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Equation of the line
Ask yourself 1) What is the y-intercept? b 2)
What is the slope? m 3) What is the rise?
numerator of slope 4) What is the run?
denominator of slope
-2
3
1
Write down your answers, you will need them for
the next step.
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Step 1 Plot the y-intercept.
Step 2 Rise 3 and then run 1. Plot your second
point.
Step 3 Connect the points with a line.
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Quiz
Soyou think that you know all about graphing?
Well, prove it! Take the 3 question quiz! After
you have graphed each line, you will be shown the
correct graph. You will be given the
opportunity to get a reminder or to move on.
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Question 1
Given the equation of the line
1) State the y-intercept. 2) State the slope. 3)
From the slope, identify the rise and the run.
4) On your graph paper, graph the line.
Check your graph
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rise
y-intercept
run
Need a reminder
Move on
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Here are the steps. Write them down.
Step 1 Plot the y-intercept. 1
Step 2 Rise -3 and then run 4. Plot your second
point.
Step 3 Connect the points with a line.
Go to Question 2
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Question 2
Given the equation of the line
1) State the y-intercept. 2) State the slope. 3)
From the slope, identify the rise and the run.
4) On your graph paper, graph the line.
Check your graph
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rise
y-intercept
run
Need a reminder
Move on
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Here are the steps. Write them down.
Step 1 Plot the y-intercept. 2
Step 2 Rise 1 and then run 3. Plot your second
point.
Step 3 Connect the points with a line.
Go to Question 3
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Question 3
Given the equation of the line
1) State the y-intercept. 2) State the slope. 3)
From the slope, identify the rise and the run.
This is tricky. Think about equivalent
fractions. 4) On your graph paper, graph the
line.
Check your graph
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rise
y-intercept
run
Need a reminder
Move on
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Here are the steps. Write them down.
Step 1 Plot the y-intercept. -4
Step 2 Rise 2 and then run 1. Plot your second
point.
Step 3 Connect the points with a line.
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Standard form to slope-intercept form
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Forms of equations of lines

• Slope-intercept form
• Note y is isolated

• Standard form
• Note A, B and C are integers

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Converting from to

• Step 1 Isolate the y-term by subtracting the
  x term from both sides of the sign.
• Step 2 Isolate the variable y by dividing all
  terms by the coefficient of y.

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Example 1
Convert
to slope-intercept form.
Step 1 Isolate the y-term by subtracting the x
term from both sides of the sign.
Step 2 Isolate the variable y by dividing all
terms by the coefficient of y.
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Lets try it together!

• Get out your graph paper and pencil.
• We are going to try to convert the form together.
• Write down the question and your work for each
  step.
• Ready?
• Lets GO!

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Example 2
Convert
to slope-intercept form.
Step 1 Isolate the y-term by subtracting the x
term from both sides of the sign.
Step 2 Isolate the variable y by dividing all
terms by the coefficient of y.
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Check your work.
Step 1 Isolate the y-term by subtracting the x
term from both sides of the sign.
Step 2 Isolate the variable y by dividing all
terms by the coefficient of y.
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Quiz
Soyou think that you know all about
converting from standard to slope-intercept form?
Well, prove it! Take the 3 question quiz! You
will need to write the question on your paper and
then show your work to convert forms.
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Question 1
Note The button to move on will come up 10
seconds after you are given the question. Do not
move on until you are finished the conversion
from standard to slope-intercept form.
Convert
to slope-intercept form.
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Check your steps and the answer.
Step 1
Step 2
The answer
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Question 2
Note The button to move on will come up 10
seconds after you are given the question. Do not
move on until you are finished the conversion
from standard to slope-intercept form.
Convert
to slope-intercept form.
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Check your steps and the answer.
Step 1
Step 2
The answer
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Question 3
Note The button to move on will come up 10
seconds after you are given the question. Do not
move on until you are finished the conversion
from standard to slope-intercept form.
Convert
to slope-intercept form.
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Check your steps and the answer.
Step 1
Step 2
The answer
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What we learned

• 1) To identify slope and y-intercept when given
  the equation of a line in slope-intercept form.
• 2) To graph a line when given the equation in
  slope-intercept form.
• 3) To convert from standard form to slope
  intercept form.

Now what?
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Reason it out!

• -You will be given three equations of lines in
• standard form.
• -Put together all the knowledge that you gained
• and graph the three lines on a fresh sheet of
  graph
• paper. Be sure to show all your work.
• -Give me your graph paper so I may check it.

I am READY!!!
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Final Quiz

• On separate coordinate planes, graph each
• of the three lines that are described by the
• equations below.

1)
2)
3)
Now what?
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Yahoo!!!
Great Work!
Fabulous!
You did it!
Unbelievable!
You are amazing!
Give me your three graphed lines now.