Question 132894


{{{1*x+5*y=10}}} 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+5*(0)=10}}} Plug in {{{y=0}}}


{{{1*x=10}}} Simplify


{{{x=10/1}}} Divide both sides by 1



{{{x=10}}} Reduce




So the x-intercept is *[Tex \Large \left(10,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{1*x+5*y=10}}} 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)+5*y=10}}} Plug in {{{x=0}}}


{{{5*y=10}}} Simplify


{{{x=10/5}}} Divide both sides by 5




{{{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(10,0\right)]


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




Now plot the two points *[Tex \Large \left(10,0\right)] and *[Tex \Large \left(0,2\right)] 


{{{drawing(500, 500, -12, 12, -4, 4,
graph(500, 500, -12, 12, -4, 4,0),
circle(10,0,0.133333333333333),
circle(10,0,0.163333333333333),

circle(0,2,0.133333333333333),
circle(0,2,0.163333333333333)


)}}}



Now draw a line through the two points to graph {{{1*x+5*y=10}}}

{{{drawing(500, 500, -12, 12, -4, 4,
graph(500, 500, -12, 12, -4, 4,(10-1*x)/5),
circle(10,0,0.133333333333333),
circle(10,0,0.163333333333333),

circle(0,2,0.133333333333333),
circle(0,2,0.163333333333333)


)}}} graph of {{{1*x+5*y=10}}} through the points *[Tex \Large \left(10,0\right)] and *[Tex \Large \left(0,2\right)]