Question 588571
I'm assuming you want to find the x and y intercepts so you can graph.

<h4>x-intercept</h4>

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



{{{-4x-5y=30}}} Start with the given equation.



{{{-4x-5(0)=30}}} Plug in {{{y=0}}}.



{{{-4x-0=30}}} Multiply {{{-5}}} and 0 to get 0.



{{{-4x=30}}} Simplify.



{{{x=(30)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{x}}}.



{{{x=-15/2}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(-\frac{15}{2},0\right)].



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<h4>y-intercept</h4>

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



{{{-4x-5y=30}}} Start with the given equation.



{{{-4(0)-5y=30}}} Plug in {{{x=0}}}.



{{{-0-5y=30}}} Multiply {{{-4}}} and 0 to get 0.



{{{-5y=30}}} Simplify.



{{{y=(30)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=-6}}} Reduce.



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



Now let's plot the points *[Tex \LARGE \left(-\frac{15}{2},0\right)] and *[Tex \LARGE \left(0,-6\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(-15/2,0,0.03),circle(-15/2,0,0.05),circle(-15/2,0,0.08),circle(-15/2,0,0.10),circle(-15/2,0,0.12),
circle(0,-6,0.03),circle(0,-6,0.05),circle(0,-6,0.08),circle(0,-6,0.10),circle(0,-6,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{-4x-5y=30}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(30+4x)/(-5)),
circle(-15/2,0,0.03),circle(-15/2,0,0.05),circle(-15/2,0,0.08),circle(-15/2,0,0.10),circle(-15/2,0,0.12),
circle(0,-6,0.03),circle(0,-6,0.05),circle(0,-6,0.08),circle(0,-6,0.10),circle(0,-6,0.12)
)}}} Graph of {{{-4x-5y=30}}}


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