Question 536752


<h4>x-intercept</h4>

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



{{{-5x+9y=-45}}} Start with the given equation.



{{{-5x+9(0)=-45}}} Plug in {{{y=0}}}.



{{{-5x+0=-45}}} Multiply {{{9}}} and 0 to get 0.



{{{-5x=-45}}} Simplify.



{{{x=(-45)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}.



{{{x=9}}} Reduce.



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



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<h4>y-intercept</h4>

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



{{{-5x+9y=-45}}} Start with the given equation.



{{{-5(0)+9y=-45}}} Plug in {{{x=0}}}.



{{{-0+9y=-45}}} Multiply {{{-5}}} and 0 to get 0.



{{{9y=-45}}} Simplify.



{{{y=(-45)/(9)}}} Divide both sides by {{{9}}} to isolate {{{y}}}.



{{{y=-5}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-5\right)].



Now let's plot the points *[Tex \LARGE \left(9,0\right)] and *[Tex \LARGE \left(0,-5\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(9,0,0.03),circle(9,0,0.05),circle(9,0,0.08),circle(9,0,0.10),circle(9,0,0.12),
circle(0,-5,0.03),circle(0,-5,0.05),circle(0,-5,0.08),circle(0,-5,0.10),circle(0,-5,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{-5x+9y=-45}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(-45+5x)/(9)),
circle(9,0,0.03),circle(9,0,0.05),circle(9,0,0.08),circle(9,0,0.10),circle(9,0,0.12),
circle(0,-5,0.03),circle(0,-5,0.05),circle(0,-5,0.08),circle(0,-5,0.10),circle(0,-5,0.12)
)}}} Graph of {{{-5x+9y=-45}}}



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