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Converting Y=mx+b to standard form

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Dividing both sides of 60x + 30y = 15 by 15:
4x + 2y = 1
This is in the "Standard Form" of the linear equation.
"Slope-Intercept Form" is y = mx + b, where m is the slope and b is the y-intercept.
Subtract 4x from both sides:
4x - 4x + 2y = 1 - 4x
Divide both sides by 2:
y = 1/2 - 2x or y = -2x + 1/2
The slope is -2 and the y-intercept is 1/2.
Standard Form can represent any line, including x = 3, a vertical line. Slope-Intercept Form cannot represent a vertical line, but otherwise it's very useful for generating points to graph. Just start by graphing the y-intercept point, (0,b), then use the slope to create another point, and another, ...
Hi Ben,

I believe that the confusion comes from a simple mistake made early on when trying to solve this problem.

The problem is that you want your equation in a y = mx + b format, if I'm not mistaken.

Your example is:
60x + 30y = 15

If you subtract the term with y as you suggest, you should get:
60x = 15 - 30y

Then in order to isolate the term with y, you would need to subtract 15 from both sides to give:
60x - 15 = -30y

Now in order to "solve for y", you would divide by negative 30 to give you the final answer:
-2x + 1/2 = y

An easier way to solve this is to subtract the term 60x in the first place to get y alone, and then divide by positive 30.

Hope that this was helpful, and good luck in your work.