Question 117179


{{{-2*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:

{{{-2*x+5*(0)=10}}} Plug in {{{y=0}}}


{{{-2*x=10}}} Simplify


{{{x=10/-2}}} Divide both sides by -2



{{{x=-5}}} Reduce




So the x-intercept is *[Tex \Large \left(-5,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{-2*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:

{{{-2*(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(-5,0\right)]


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




Now plot the two points *[Tex \Large \left(-5,0\right)] and *[Tex \Large \left(0,2\right)] 


{{{drawing(500, 500, -7, 7, -4, 4,
graph(500, 500, -7, 7, -4, 4,0),
circle(-5,0,0.0777777777777778),
circle(-5,0,0.107777777777778),

circle(0,2,0.0777777777777778),
circle(0,2,0.107777777777778)


)}}}



Now draw a line through the two points to graph {{{-2*x+5*y=10}}}

{{{drawing(500, 500, -7, 7, -4, 4,
graph(500, 500, -7, 7, -4, 4,(10--2*x)/5),
circle(-5,0,0.0777777777777778),
circle(-5,0,0.107777777777778),

circle(0,2,0.0777777777777778),
circle(0,2,0.107777777777778)


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