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Equations – Solving for Y

Equations – Solving for Y. How to write every equation in y = mx + b form. 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 you’re talking).

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Equations – Solving for Y

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  1. Equations – Solving for Y How to write every equation in y = mx + b form

  2. 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 you’re talking)

  3. 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?

  4. Notice, Y should be the only variable on the left hand side. • Y = mx + b Not a very friendly letter is it?

  5. 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.

  6. Remember…. An equation is balanced. It’s a statement that says one side is equal to the other. Think of a scale.

  7. 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

  8. Solving for y • Subtract 2x from the left side. 2x -2x + y = 10

  9. Solving for y • What happened? The equation isn’t balanced anymore. We only took 2x from the left side. y = 10

  10. Solving for y • Subtract 2x from the right side also. Now the variable y is all by itself. y = 10 -2x

  11. 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?

  12. Try another one • 4x = -y + 2 Remember, we want y all by itself on the left side.

  13. 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

  14. Next step? • 4x + y = 2 Better subtract 4x from both sides 4x – 4x + y = 2 - 4x Y = 2 – 4x

  15. Almost done Y = 2 – 4x Y = -4x + 2 Close, we just need to switch two numbers now. You did it!

  16. 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?}

  17. Two more steps • 3y = 12 + 6x I still need y by itself so let’s divide everything by 3. Y = 4 + 2x One more step

  18. Y = 4 + 2x Y = 2x + 4 You did it!

  19. Now do these on your own • 2 = -y + 3x • 2y – 8x = 2 3)2x + 3y = 3

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