SOLUTION: How do i put 2/3x + 2y = 8 into y=mx+b?

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Question 1053541: How do i put 2/3x + 2y = 8 into y=mx+b?
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F3%29x%2B2y=8
Subtract -%282%2F3%29x from both sides,
2y=-%282%2F3%29x%2B8
Divide both side by 2.
y=-%281%2F3%29x%2B4
Done!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Algebra of each step


Step 1: %282%2F3%29x+%2B+2y+=+8


Step 2: %282%2F3%29x+%2B+2y-%282%2F3%29x+=+8-%282%2F3%29x


Step 3: 2y+=+-%282%2F3%29x%2B8


Step 4: %281%2F2%29%2A2y+=+%281%2F2%29%2A%28-%282%2F3%29x%2B8%29


Step 5: y+=+%281%2F2%29%2A%28-%282%2F3%29x%29%2B%281%2F2%29%2A%288%29


Step 6: y+=+%28-1%2F3%29x%2B%281%2F2%29%2A%288%29


Step 7: y+=+%28-1%2F3%29x%2B4


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Explanation of the steps above


Step 1: Original equation (No work done so far)


Step 2: Subtract %282%2F3%29x from both sides


Step 3: Combine like terms on the left side. Notice how the x terms on the left side combine to 0x = 0 and they effectively go away. On the right side, I simply flipped the terms.


Step 4: Multiply both sides by 1%2F2 to isolate y. Note: %281%2F2%29%2A%282%29+=+2%2F2+=+1


Step 5: Distribute


Step 6: Multiply 1%2F2 with -%282%2F3%29x to get


Step 7: Multiply 1%2F2 with 8 to get %281%2F2%29%2A8+=+%281%2F2%29%2A%288%2F1%29+=+%281%2A8%29%2F%282%2A1%29+=+8%2F2+=+4


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After those 7 steps, the equation %282%2F3%29x+%2B+2y+=+8 turns into y+=+%28-1%2F3%29x%2B4


The final answer is y+=+%28-1%2F3%29x%2B4


In this case, the equation is in the form y+=+mx%2Bb where the slope is m+=+-1%2F3 and the y intercept is b+=+4