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!
