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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 = 99 (a little harder) 2x + y = 34 (now you’re 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 There’s too much on the left hand side.
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Remember…. An equation is balanced. It’s 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 isn’t 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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all by itself on the left side.
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 I’m 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 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 = x 3y = x {Now what?}
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Two more steps Y = 4 + 2x 3y = 12 + 6x One more step
I still need y by itself so let’s 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
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