Question 134276
{{{3x-9=3y }}} Start with the given equation




{{{3x-9-3y=0 }}} Subtract 3y from both sides



{{{3x-3y=9 }}} Add 9 to both sides



So the equation is in standard form





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


Let's find the x-intercept


To find the x-intercept, let y=0 and solve for x:

{{{3*x-3*(0)=9}}} Plug in {{{y=0}}}


{{{3*x=9}}} Simplify


{{{x=9/3}}} Divide both sides by 3



{{{x=3}}} Reduce




So the x-intercept is *[Tex \Large \left(3,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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


Now let's find the y-intercept


To find the y-intercept, let x=0 and solve for y:

{{{3*(0)-3*y=9}}} Plug in {{{x=0}}}


{{{3*y=9}}} Simplify


{{{x=9/-3}}} Divide both sides by -3




{{{y=-3}}} Reduce




So the y-intercept is *[Tex \Large \left(0,-3\right)] (note: the y-intercept will always have a x-coordinate equal to zero)


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So we have these intercepts:

x-intercept: *[Tex \Large \left(3,0\right)]


y-intercept: *[Tex \Large \left(0,-3\right)]




Now plot the two points *[Tex \Large \left(3,0\right)] and *[Tex \Large \left(0,-3\right)] 


{{{drawing(500, 500, -5, 5, -5, 5,
graph(500, 500, -5, 5, -5, 5,0),
circle(3,0,0.0666666666666667),
circle(3,0,0.0966666666666667),

circle(0,-3,0.0666666666666667),
circle(0,-3,0.0966666666666667)


)}}}



Now draw a line through the two points to graph {{{3*x-3*y=9}}}

{{{drawing(500, 500, -5, 5, -5, 5,
graph(500, 500, -5, 5, -5, 5,(9-3*x)/-3),
circle(3,0,0.0666666666666667),
circle(3,0,0.0966666666666667),

circle(0,-3,0.0666666666666667),
circle(0,-3,0.0966666666666667)


)}}} graph of {{{3*x-3*y=9}}} through the points *[Tex \Large \left(3,0\right)] and *[Tex \Large \left(0,-3\right)]