Question 125736
{{{6*x+1*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:

{{{6*x+1*(0)=6}}} Plug in {{{y=0}}}


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


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



{{{x=1}}} Reduce




So the x-intercept is *[Tex \Large \left(1,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{6*x+1*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:

{{{6*(0)+1*y=6}}} Plug in {{{x=0}}}


{{{1*y=6}}} Simplify


{{{x=6/1}}} Divide both sides by 1




{{{y=6}}} Reduce




So the y-intercept is *[Tex \Large \left(0,6\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(1,0\right)]


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




Now plot the two points *[Tex \Large \left(1,0\right)] and *[Tex \Large \left(0,6\right)] 


{{{drawing(500, 500, -3, 3, -8, 8,
graph(500, 500, -3, 3, -8, 8,0),
circle(1,0,0.03),
circle(1,0,0.05),

circle(0,6,0.03),
circle(0,6,0.05)


)}}}



Now draw a line through the two points to graph {{{6*x+1*y=6}}}

{{{drawing(500, 500, -3, 3, -8, 8,
graph(500, 500, -3, 3, -8, 8,(6-6*x)/1),
circle(1,0,0.03),
circle(1,0,0.05),

circle(0,6,0.03),
circle(0,6,0.05)


)}}} graph of {{{6*x+1*y=6}}} through the points *[Tex \Large \left(1,0\right)] and *[Tex \Large \left(0,6\right)]