Question 119695
#1




{{{2*x+3*y=6}}} Start with the given equation


Let's find the x-intercept


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

{{{2*x+3*(0)=6}}} Plug in {{{y=0}}}


{{{2*x=6}}} Simplify


{{{x=6/2}}} Divide both sides by 2



{{{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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{{{2*x+3*y=6}}} Start with the given equation


Now let's find the y-intercept


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

{{{2*(0)+3*y=6}}} Plug in {{{x=0}}}


{{{3*y=6}}} Simplify


{{{x=6/3}}} Divide both sides by 3




{{{y=2}}} Reduce




So the y-intercept is *[Tex \Large \left(0,2\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(0,2\right)]




Now plot the two points *[Tex \Large \left(3,0\right)] and *[Tex \Large \left(0,2\right)] 


{{{drawing(500, 500, -5, 5, -4, 4,
graph(500, 500, -5, 5, -4, 4,0),
circle(3,0,0.0555555555555556),
circle(3,0,0.0855555555555556),

circle(0,2,0.0555555555555556),
circle(0,2,0.0855555555555556)


)}}}



Now draw a line through the two points to graph {{{2*x+3*y=6}}}

{{{drawing(500, 500, -5, 5, -4, 4,
graph(500, 500, -5, 5, -4, 4,(6-2*x)/3),
circle(3,0,0.0555555555555556),
circle(3,0,0.0855555555555556),

circle(0,2,0.0555555555555556),
circle(0,2,0.0855555555555556)


)}}} graph of {{{2*x+3*y=6}}} through the points *[Tex \Large \left(3,0\right)] and *[Tex \Large \left(0,2\right)]





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#2




{{{2*x-3*y=12}}} Start with the given equation


Let's find the x-intercept


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

{{{2*x-3*(0)=12}}} Plug in {{{y=0}}}


{{{2*x=12}}} Simplify


{{{x=12/2}}} Divide both sides by 2



{{{x=6}}} Reduce




So the x-intercept is *[Tex \Large \left(6,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{2*x-3*y=12}}} Start with the given equation


Now let's find the y-intercept


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

{{{2*(0)-3*y=12}}} Plug in {{{x=0}}}


{{{3*y=12}}} Simplify


{{{x=12/-3}}} Divide both sides by -3




{{{y=-4}}} Reduce




So the y-intercept is *[Tex \Large \left(0,-4\right)] (note: the y-intercept will always have a x-coordinate equal to zero)


------------------------------------------


So we have these intercepts:

x-intercept: *[Tex \Large \left(6,0\right)]


y-intercept: *[Tex \Large \left(0,-4\right)]




Now plot the two points *[Tex \Large \left(6,0\right)] and *[Tex \Large \left(0,-4\right)] 


{{{drawing(500, 500, -8, 8, -6, 6,
graph(500, 500, -8, 8, -6, 6,0),
circle(6,0,0.111111111111111),
circle(6,0,0.141111111111111),

circle(0,-4,0.111111111111111),
circle(0,-4,0.141111111111111)


)}}}



Now draw a line through the two points to graph {{{2*x-3*y=12}}}

{{{drawing(500, 500, -8, 8, -6, 6,
graph(500, 500, -8, 8, -6, 6,(12-2*x)/-3),
circle(6,0,0.111111111111111),
circle(6,0,0.141111111111111),

circle(0,-4,0.111111111111111),
circle(0,-4,0.141111111111111)


)}}} graph of {{{2*x-3*y=12}}} through the points *[Tex \Large \left(6,0\right)] and *[Tex \Large \left(0,-4\right)]