Question 189820
{{{-(2/3)x+4y=8/3}}} Start with the given equation.



{{{cross(3)(-(2/cross(3))x)+3(4y)=cross(3)(8/cross(3))}}} Multiply EVERY term by the LCD 3 to clear the fractions



{{{-2x+3(4y)=8}}} Simplify



{{{-2x+12y=8}}} Multiply



{{{12y=8+2x}}} Add {{{2x}}} to both sides.



{{{12y=2x+8}}} Rearrange the terms.



{{{y=(2x+8)/(12)}}} Divide both sides by {{{12}}} to isolate y.



{{{y=(2/(12))x+(8)/(12)}}} Break up the fraction.



{{{y=(1/6)x+2/3}}} Reduce.



So the equation {{{y=(1/6)x+2/3}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=1/6}}} and the y-intercept is {{{b=2/3}}} 


note: the y-intercept is the point *[Tex \LARGE \left(0,\frac{2}{3}\right)]