Question 118261


{{{3*x-1*y=3}}} 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-1*(0)=3}}} Plug in {{{y=0}}}


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


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



{{{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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{{{3*x-1*y=3}}} 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)-1*y=3}}} Plug in {{{x=0}}}


{{{1*y=3}}} Simplify


{{{x=3/-1}}} Divide both sides by -1




{{{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(1,0\right)]


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




Now plot the two points *[Tex \Large \left(1,0\right)] and *[Tex \Large \left(0,-3\right)] 


{{{drawing(500, 500, -3, 3, -5, 5,
graph(500, 500, -3, 3, -5, 5,0),
circle(1,0,0.0444444444444444),
circle(1,0,0.0744444444444445),

circle(0,-3,0.0444444444444444),
circle(0,-3,0.0744444444444445)


)}}}



Now draw a line through the two points to graph {{{3*x-1*y=3}}}

{{{drawing(500, 500, -3, 3, -5, 5,
graph(500, 500, -3, 3, -5, 5,(3-3*x)/-1),
circle(1,0,0.0444444444444444),
circle(1,0,0.0744444444444445),

circle(0,-3,0.0444444444444444),
circle(0,-3,0.0744444444444445)


)}}} graph of {{{3*x-1*y=3}}} through the points *[Tex \Large \left(1,0\right)] and *[Tex \Large \left(0,-3\right)]