Question 166501


<h4>x-intercept</h4>

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{-5x - 10y = 10}}} Start with the given equation.



{{{-5x - 10(0) = 10}}} Plug in {{{y=0}}}.



{{{-5x - 0 = 10}}} Multiply {{{10}}} and 0 to get 0.



{{{-5x - 0 = 10}}} Simplify.



{{{-5x=10+0}}} Add {{{0}}} to both sides.



{{{-5x=10}}} Combine like terms on the right side.



{{{x=(10)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}.



{{{x=-2}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(-2,0\right)].



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<h4>y-intercept</h4>

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{-5x - 10y = 10}}} Start with the given equation.



{{{-5(0) - 10y = 10}}} Plug in {{{x=0}}}.



{{{-0 - 10y = 10}}} Multiply {{{-5}}} and 0 to get 0.



{{{ - 10y = 10}}} Simplify.



{{{y=(10)/(-10)}}} Divide both sides by {{{-10}}} to isolate {{{y}}}.



{{{y=-1}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-1\right)].





Now plot the two points *[Tex \Large \left(-2,0\right)] and *[Tex \Large \left(0,-1\right)] 


{{{drawing(500, 500, -4, 4, -3, 3,
graph(500, 500, -4, 4, -3, 3,0),
circle(-2,0,0.0333333333333333),
circle(-2,0,0.0633333333333333),

circle(0,-1,0.0333333333333333),
circle(0,-1,0.0633333333333333)


)}}}



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

{{{drawing(500, 500, -4, 4, -3, 3,
graph(500, 500, -4, 4, -3, 3,(10--5*x)/-10),
circle(-2,0,0.0333333333333333),
circle(-2,0,0.0633333333333333),

circle(0,-1,0.0333333333333333),
circle(0,-1,0.0633333333333333)


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