Equations

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Equations Solving for Y

• How to write every equation in y mx b form

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An equation is a sentence that always has an
equal sign.
Sample equations

• 3 4 7 (not very difficult)

• x -45 99 (a little harder)

• 2x y 34 (now youre talking)

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Changing an equation to be in Slope Y-intercept
form.

• In order for an equation to be in slope
  y-intercept form it has to look like this.

Y mx b

• What does m stand for?

• What does b stand for?

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Notice, Y should be the only variable on the left
hand side.

• Y mx b

Not a very friendly letter is it?
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But what happens when the y is not all alone?

• How to change equations to be in the slope
  y-intercept form

For example 2x y 10

• Theres too much on the left hand side.

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Remember.

• An equation is balanced. Its a statement
  that says one side is equal to the other. Think
  of a scale.

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Solving for y

• This equation is balanced right now but we have
  to get rid of the 2x on the left side.

• 2x y 10

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Solving for y

• Subtract 2x from the left side.

• 2x -2x y 10

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Solving for y

• What happened? The equation isnt balanced
  anymore. We only took 2x from the left side.

• y 10

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Solving for y

• Subtract 2x from the right side also. Now the
  variable y is all by itself.

• y 10 -2x

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Solving for y

• Move the -2x in front of 10 and we have the
  correct form. Y mx b

• y -2x 10

What is the slope?
What is the y-intercept?
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Try another one

• 4x -y 2

Remember, we want y all by itself on the left
side.
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Move the y over to the left

• 4x -y 2

• Add y to both sides to keep everything balanced
• 4x y -y y 2
• 4x y 2

Make sure Im still balanced
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Next step?

• 4x y 2
• Better subtract 4x from both sides
• 4x 4x y 2 - 4x
• Y 2 4x

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Almost done

• Y 2 4x
• Y -4x 2

Close, we just need to switch two numbers now.
You did it!
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What if they get more difficult?

• Like 3y - 6x 12
• Do the same thing, isolated y on the left hand
  side by adding 6x to both sides.
• 3y - 6x 6x 12 6x
• 3y 12 6x Now what?

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Two more steps

• 3y 12 6x
• I still need y by itself so lets divide
  everything by 3.

Y 4 2x
One more step
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• Y 4 2x
• Y 2x 4

You did it!
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Now do these on your own

• 2 -y 3x
• 2y 8x 2
• 3)2x 3y 3