Question 118259


{{{4*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:

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


{{{4*x=12}}} Simplify


{{{x=12/4}}} Divide both sides by 4



{{{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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{{{4*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:

{{{4*(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)


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So we have these intercepts:

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


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




Now plot the two points *[Tex \Large \left(3,0\right)] and *[Tex \Large \left(0,-4\right)] 


{{{drawing(500, 500, -5, 5, -6, 6,
graph(500, 500, -5, 5, -6, 6,0),
circle(3,0,0.0777777777777778),
circle(3,0,0.107777777777778),

circle(0,-4,0.0777777777777778),
circle(0,-4,0.107777777777778)


)}}}



Now draw a line through the two points to graph {{{4*x-3*y=12}}}

{{{drawing(500, 500, -5, 5, -6, 6,
graph(500, 500, -5, 5, -6, 6,(12-4*x)/-3),
circle(3,0,0.0777777777777778),
circle(3,0,0.107777777777778),

circle(0,-4,0.0777777777777778),
circle(0,-4,0.107777777777778)


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