1. The green rectangles will represent positive x
The green rectangles will represent positive x. The red rectangles will equal negative x. One of each will equal a neutral pair and cancel out to zero.
The purple rectangles will represent positive y. The black rectangles will equal negative y. One of each will equal a neutral pair and cancel out to zero.
The yellow squares will represent positive 1. The red squares will equal negative 1. One of each will equal a neutral pair and cancel out to zero.
Using Algebra tiles for converting from Standard form to slope intercept form
You need to understand what is going on with your work when you convert equations in order to understand why they are equal.

2. Example 1
4x + 2y = 8 =
You want to eventually find out how much one purple tile is worth.
If you can combine anything on either side of the equal sign first, you should do that. In this case there are no like terms to combine. You need to now get the purple tiles alone. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away. You can add 4 negative x tiles on each side to keep your equations balanced.

3. Example 1
4x + 2y = 8 =
You want to eventually find out how much one purple tile is worth.
You If you can combine anything on either side of the equal sign first, you should do that. In this case there are no like terms to combine. You need to now get the purple tiles alone. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away. You can add 4 negative x tiles on each side to keep your equations balanced.

4. Example 1
4x + 2y = 8 =
You want to eventually find out how much one purple tile is worth.
You If you can combine anything on either side of the equal sign first, you should do that. In this case there are no like terms to combine. You need to now get the purple tiles alone. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away. You can add 4 negative x tiles on each side to keep your equations balanced.

5. Example 1
4x + 2y = 8 =
You now need to now find out how much one purple tile is worth.
If 2 purple tiles are worth the same value as 8 yellow and 4 red, then 1 purple is worth 4 yellow and 2 red.

6. Example 1
4x + 2y = 8 =
4x + 2y = 8
-4x x
2y = -4x + 8
y = -2x + 4

7. Example 1
4x + 2y = 8
4x + 2y = 8
-4x x
2y = -4x + 8
y = -2x + 4

8. What is the first step you should do?
Example 2
6x + 3y = 15 =
You want to eventually find out how much one purple tile is worth.
If you can combine anything on either side of the equal sign first, you should do that. In this case there are no like terms to combine. You need to now get the purple tiles alone. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away.
What is the first step you should do?

9. Example 2
6x + 3y = 15 =

10. Example 2
After adding 6 negative x’s on both sides, the positive x’s canceled out on the left, and the negative x’s remained on the right.
You now have 3ys on the left, and 15 unit squares and 6 negative x’s on the right.
How much is one positive y worth?
6x + 3y = 15 =

11. 6x + 3y = 15 = 6x + 3y = 15 -6x -6x 3y = -6x + 15 y = -2x + 5
Example 2
6x + 3y = 15
After adding 6 negative x’s on both sides, the positive x’s canceled out on the left, and the negative x’s remained on the right.
You now have 3ys on the left, and 15 unit squares and 6 negative x’s on the right.
How much is one positive y worth? =
6x + 3y = 15
-6x x
3y = -6x + 15
y = -2x + 5

12. Example 2
6x + 3y = 15
6x + 3y = 15
-6x x
3y = -6x + 15
y = -2x + 5

13. What is the next step you should do?
Example 3
2x - y + x = 7 3x – y = 7 =
You want to eventually find out how much one purple tile is worth.
If you can combine anything on either side of the equal sign first, you should do that. This time you can combine like terms. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away.
What is the next step you should do?

14. What is the next step you should do?
Example 3
2x - y + x = 7 3x – y = 7 =
You want to eventually find out how much one purple tile is worth.
If you can combine anything on either side of the equal sign first, you should do that. This time you can combine like terms. Since you do not have green tiles on both side, you cannot just take them off. You need to make neutral pairs to make the green tiles on the left go away.
What is the next step you should do?

15. Example 3
2x - y + x = 7 3x – y = 7 =
You need to know how much a purple tile is worth, but you have a black one left instead of purple ones.
You need to find the opposite of what is on the board.

16. = 3x - y = 7 -3x -3x -y = -3x + 7 y = 3x + (-7)
Example 3
2x - y + x = 7 3x – y = 7 =
3x - y = 7
-3x x
-y = -3x + 7
y = 3x + (-7)
You need to know how much a purple tile is worth, but you have a black one left instead of purple ones.
You need to find the opposite of what is on the board.

17. 3x – y = 7 3x - y = 7 -3x -3x -y = -3x + 7 y = 3x + (-7)
Example 3
3x – y = 7
2x - y + x = 7
3x - y = 7
-3x x
-y = -3x + 7
y = 3x + (-7)

18. Example 4
-5x - 2y = -10 3x – y = 7 =

19. Example 4
-5x - 2y = -10 3x – y = 7 =

20. Example 4
-5x - 2y = -10 3x – y = 7 =

21. Example 4
-5x - 2y = -10 3x – y = 7 =

22. = -5x - 2y = -10 +5x +5x -2y = 5x + (-10) -y = 2.5x + (-5)
Example 4
-5x - 2y = -10 3x – y = 7 =
-5x - 2y = -10
+5x x
-2y = 5x + (-10)
-y = 2.5x + (-5)
y = -2.5x + 5

23. -5x - 2y = -10 3x – y = 7 -5x - 2y = -10 +5x +5x -2y = 5x + (-10)
Example 4
-5x - 2y = -10 3x – y = 7
-5x - 2y = -10
+5x x
-2y = 5x + (-10)
-y = 2.5x + (-5)
y = -2.5x + 5