Question 113840


{{{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)]