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 = 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. all by itself on the left side.
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 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 = x
3y = x {Now what?}

17. 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

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