Question 143137
{{{3x-2y=6}}} Start with the given equation



{{{-2y=6-3x}}}  Subtract {{{3 x}}} from both sides



{{{-2y=-3x+6}}} Rearrange the equation



{{{y=(-3x+6)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=(-3/-2)x+(6)/(-2)}}} Break up the fraction



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





In order to graph this equation, we only need two points to create a straight line





--------------------------------Let's find the first point--------------------------------


{{{y=(3/2)x-3}}} Start with the given equation





{{{y=(3/2)(0)-3}}} Plug in {{{x=0}}} (you can start with any number, but zero is the easiest number to work with since anything multiplied by zero is zero)





{{{y=0-3}}} Multiply {{{3/2}}} and {{{0}}} to get {{{0}}}





{{{y=-3}}} Subtract 




So when {{{x=0}}}, we have the value {{{y=-3}}}. This means we have the first point *[Tex \LARGE \left(0,-3\right)]





--------------------------------Let's find the second point--------------------------------


{{{y=(3/2)x-3}}} Start with the given equation





{{{y=(3/2)(2)-3}}} Plug in {{{x=2}}} 





{{{y=6/2-3}}} Multiply {{{3/2}}} and {{{2}}} to get {{{6/2}}}





{{{y=3-3}}} Reduce {{{6/2}}} to get {{{3}}}





{{{y=0}}} Subtract 




So when {{{x=2}}}, we have the value {{{y=0}}}. This means we have the second point *[Tex \LARGE \left(2,0\right)]





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So we have the two points: *[Tex \LARGE \left(0,-3\right)] and *[Tex \LARGE \left(2,0\right)]



Now plot these two points on a coordinate system


{{{drawing(500,500,-9,11,-9,11,
graph(500,500,-9,11,-9,11,0),
grid(1),
circle(0,-3,0.1),
circle(0,-3,0.12),
circle(0,-3,0.15),
circle(2,0,0.1),
circle(2,0,0.12),
circle(2,0,0.15)
) }}}




Now draw a straight line through the two points. This line is the graph of {{{y=(3/2)x-3}}}


{{{drawing(500,500,-9,11,-9,11,
graph(500,500,-9,11,-9,11,(3/2)x-3),
grid(1),
circle(0,-3,0.1),
circle(0,-3,0.12),
circle(0,-3,0.15),
circle(2,0,0.1),
circle(2,0,0.12),
circle(2,0,0.15)
) }}} Graph of {{{y=(3/2)x-3}}} through the two points *[Tex \LARGE \left(0,-3\right)] and *[Tex \LARGE \left(2,0\right)]