Question 134284

{{{-1*x+4*y=8}}} 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+4*(0)=8}}} Plug in {{{y=0}}}


{{{-1*x=8}}} Simplify


{{{x=8/-1}}} Divide both sides by -1



{{{x=-8}}} Reduce




So the x-intercept is *[Tex \Large \left(-8,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{-1*x+4*y=8}}} 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)+4*y=8}}} Plug in {{{x=0}}}


{{{-4*y=8}}} Simplify


{{{x=8/4}}} Divide both sides by 4




{{{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(-8,0\right)]


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




Now plot the two points *[Tex \Large \left(-8,0\right)] and *[Tex \Large \left(0,2\right)] 


{{{drawing(500, 500, -10, 10, -4, 4,
graph(500, 500, -10, 10, -4, 4,0),
circle(-8,0,0.111111111111111),
circle(-8,0,0.141111111111111),

circle(0,2,0.111111111111111),
circle(0,2,0.141111111111111)


)}}}



Now draw a line through the two points to graph {{{-1*x+4*y=8}}}

{{{drawing(500, 500, -10, 10, -4, 4,
graph(500, 500, -10, 10, -4, 4,(8--1*x)/4),
circle(-8,0,0.111111111111111),
circle(-8,0,0.141111111111111),

circle(0,2,0.111111111111111),
circle(0,2,0.141111111111111)


)}}} graph of {{{-1*x+4*y=8}}} through the points *[Tex \Large \left(-8,0\right)] and *[Tex \Large \left(0,2\right)]