Question 755164
I do not see the "following equation", so I guess it did not follow.
 
The slope intercept form is the form that starts with y= ...
To get to that form from any other form of the equation, you just "solve for y".
 
The equation in slope-intercept form looks like
y = mx + b
The number m that is multiplied times x is called the slope.
The number b that is added to the product of m times x is called the intercept.
 
EXAMPLE:
{{{3x+2y=5}}} --> {{{2y=-3x+5}}} --> {{{y=(-3x+5)/2}}} --> {{{y=(-3/2)x+5/2}}}
The slope-intercept form of {{{3x+2y=5}}} is {{{y=(-3/2)x+5/2}}}
The slope is {{{-3/2}}}.
The intercept is {{{5/2}}}.