To write the equation of a line in slope-intercept form given an equation not written as y=mx+b, use inverse operations to solve for y. In other words, get y by itself on one side of the equal sign and move everything else to the other side of the equal sign.
There are lots of different forms of equations and it’s really useful to be able to move back and forth between different writings of the same equation in order to solve Math problems. Like for example in this situation, I’m given a problem that’s not in y equals mx plus b form, which is slope intercept form, but I’m asked to turn it into that format.
Let me just write that out so you understand what I mean. Slope intercept form is my goal, it looks like this, y is solved for, it’s all by itself, that’s what I want to do. I need to get y all by itself.
Let me rewrite this so that I have a little more space, and then we want to get y isolated, so I’m going to undo all the stuff that’s being done to y. First thing I’m going to do is get rid of that 3x business, so now I have 2y equals -3x plus 12, and then I want y all by itself its being multiplied by 2, so my next step would be to divide everything by 2.
Y is going to be -3½x plus 12/2 reduces to 6. Now I’m all done, that’s slope intercept form. This is the exact same line just written in a different format, and I like this format because I can see the slope really easily and I can see the y-intercept really easily.
So use your solving techniques to move from one form of an equation to the other, it might help you to get an equation into a form that’s more useful for you.
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