Question 925483
<h4>x-intercept</h4>

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



{{{-9x-6y=54}}} Start with the given equation.



{{{-9x-6(0)=54}}} Plug in {{{y=0}}}.



{{{-9x-0=54}}} Multiply {{{-6}}} and 0 to get 0.



{{{-9x=54}}} Simplify.



{{{x=(54)/(-9)}}} Divide both sides by {{{-9}}} to isolate {{{x}}}.



{{{x=-6}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(-6,0\right)].



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<h4>y-intercept</h4>

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



{{{-9x-6y=54}}} Start with the given equation.



{{{-9(0)-6y=54}}} Plug in {{{x=0}}}.



{{{0-6y=54}}} Multiply {{{-9}}} and 0 to get 0.



{{{-6y=54}}} Simplify.



{{{y=(54)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{y}}}.



{{{y=-9}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-9\right)].



Now let's plot the points *[Tex \LARGE \left(-6,0\right)] and *[Tex \LARGE \left(0,-9\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0)
circle(-6,0,0.03),circle(-6,0,0.05),circle(-6,0,0.08),circle(-6,0,0.10),circle(-6,0,0.12),
circle(0,-9,0.03),circle(0,-9,0.05),circle(0,-9,0.08),circle(0,-9,0.10),circle(0,-9,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{-9x-6y=54}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0,(54+9x)/(-6)),
circle(-6,0,0.03),circle(-6,0,0.05),circle(-6,0,0.08),circle(-6,0,0.10),circle(-6,0,0.12),
circle(0,-9,0.03),circle(0,-9,0.05),circle(0,-9,0.08),circle(0,-9,0.10),circle(0,-9,0.12)
)}}} Graph of {{{-9x-6y=54}}}