Question 278188
I'll do the first two to get you started.


# 1


{{{2x-3y=9}}} Start with the given equation.



{{{-3y=9-2x}}} Subtract {{{2x}}} from both sides.



{{{-3y=-2x+9}}} Rearrange the terms.



{{{y=(-2x+9)/(-3)}}} Divide both sides by {{{-3}}} to isolate y.



{{{y=((-2)/(-3))x+(9)/(-3)}}} Break up the fraction.



{{{y=(2/3)x-3}}} Reduce.



So the equation {{{y=(2/3)x-3}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=2/3}}} and the y-intercept is {{{b=-3}}} note: the y-intercept is the point *[Tex \LARGE \left(0,-3\right)]



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# 2



{{{x-4y=20}}} Start with the given equation.



{{{-4y=20-x}}} Subtract {{{x}}} from both sides.



{{{-4y=-x+20}}} Rearrange the terms.



{{{y=(-x+20)/(-4)}}} Divide both sides by {{{-4}}} to isolate y.



{{{y=((-1)/(-4))x+(20)/(-4)}}} Break up the fraction.



{{{y=(1/4)x-5}}} Reduce.



So the equation {{{y=(1/4)x-5}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=1/4}}} and the y-intercept is {{{b=-5}}} note: the y-intercept is the point *[Tex \LARGE \left(0,-5\right)]