Question 112075


{{{1*x-3*y=-4}}} Start with the given equation


Let's find the x-intercept


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

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


{{{1*x=-4}}} Simplify


{{{x=-4/1}}} Divide both sides by 1



{{{x=-4}}} Reduce




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




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{{{1*x-3*y=-4}}} Start with the given equation


Now let's find the y-intercept


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

{{{1*(0)-3*y=-4}}} Plug in {{{x=0}}}


{{{3*y=-4}}} Simplify


{{{x=-4/-3}}} Divide both sides by -3




{{{y=4/3}}} Reduce




So the y-intercept is *[Tex \Large \left(0,\frac{4}{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(-4,0\right)]


y-intercept: *[Tex \Large \left(0,\frac{4}{3}\right)]




Now plot the two points *[Tex \Large \left(-4,0\right)] and *[Tex \Large \left(0,\frac{4}{3}\right)]  (which is the point (0,1.33333333333333) in decimal form) 


{{{drawing(500, 500, -6, 6, -3.33333333333333, 3.33333333333333,
graph(500, 500, -6, 6, -3.33333333333333, 3.33333333333333,0),
circle(-4,0,0.0592592592592593),
circle(-4,0,0.0892592592592593),

circle(0,1.33333333333333,0.0592592592592593),
circle(0,1.33333333333333,0.0892592592592593)


)}}}



Now draw a line through the two points to graph {{{1*x-3*y=-4}}}

{{{drawing(500, 500, -6, 6, -3.33333333333333, 3.33333333333333,
graph(500, 500, -6, 6, -3.33333333333333, 3.33333333333333,(-4-1*x)/-3),
circle(-4,0,0.0592592592592593),
circle(-4,0,0.0892592592592593),

circle(0,1.33333333333333,0.0592592592592593),
circle(0,1.33333333333333,0.0892592592592593)


)}}} graph of {{{1*x-3*y=-4}}} through the points *[Tex \Large \left(-4,0\right)] and *[Tex \Large \left(0,\frac{4}{3}\right)]