Question 157949


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


Let's find the x-intercept


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


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



{{{x=6}}} Multiply



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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{{{x+3y=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:


{{{0+3y=6}}} Plug in {{{x=0}}}



{{{3y=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(6,0\right)]


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




Now plot the two points *[Tex \Large \left(6,0\right)] and *[Tex \Large \left(0,2\right)] 


{{{drawing(500, 500, -8, 8, -4, 4,
graph(500, 500, -8, 8, -4, 4,0),
circle(6,0,0.0888888888888889),
circle(6,0,0.118888888888889),

circle(0,2,0.0888888888888889),
circle(0,2,0.118888888888889)


)}}}



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

{{{drawing(500, 500, -8, 8, -4, 4,
graph(500, 500, -8, 8, -4, 4,(6-x)/3),
circle(6,0,0.0888888888888889),
circle(6,0,0.118888888888889),

circle(0,2,0.0888888888888889),
circle(0,2,0.118888888888889)


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