The slope-intercept form of an equation looks like the following:
#y = mx +b# , where #m# is the slope, #x# is the #x#-value, and #b# is the indication of the interval the graph is moved up or down.
So, to get the equation from #2x + 3y = 12# into slope intercept form, do the following steps:
1.) Get the #y# term all by itself.
#3y = 12 - 2x#
2.) Get the variable #y# so that there are no coefficients. This means we need to divide the whole thing by 3 to get y by itself, completely.
#y = 4 - 2/3x#
3.) Now rearrange the terms in the right side of the equall sign to get the form of #mx + b#.
#y = -2/3x +4#
Summary:
We first got the #y# term by itself (on one side of the equation). Then, we got ride of the coefficient (number before the #y# variable) by dividing it out. After that, we rearranged the terms #4# and #-2/3x# so that it forms #-2/3x + 4#. The final equation is #y = -2/3x + b#. And your equation is in the form #y = mx + b#!
