Question 741408


<h4>x-intercept</h4>

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



{{{3x+4y=-12}}} Start with the given equation.



{{{3x+4(0)=-12}}} Plug in {{{y=0}}}.



{{{3x+0=-12}}} Multiply {{{4}}} and 0 to get 0.



{{{3x=-12}}} Simplify.



{{{x=(-12)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=-4}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(-4,0\right)].



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<h4>y-intercept</h4>

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



{{{3x+4y=-12}}} Start with the given equation.



{{{3(0)+4y=-12}}} Plug in {{{x=0}}}.



{{{0+4y=-12}}} Multiply {{{3}}} and 0 to get 0.



{{{4y=-12}}} Simplify.



{{{y=(-12)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



{{{y=-3}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-3\right)].



Now let's plot the points *[Tex \LARGE \left(-4,0\right)] and *[Tex \LARGE \left(0,-3\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(-4,0,0.03),circle(-4,0,0.05),circle(-4,0,0.08),circle(-4,0,0.10),circle(-4,0,0.12),
circle(0,-3,0.03),circle(0,-3,0.05),circle(0,-3,0.08),circle(0,-3,0.10),circle(0,-3,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{3x+4y=-12}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(-12-3x)/(4)),
circle(-4,0,0.03),circle(-4,0,0.05),circle(-4,0,0.08),circle(-4,0,0.10),circle(-4,0,0.12),
circle(0,-3,0.03),circle(0,-3,0.05),circle(0,-3,0.08),circle(0,-3,0.10),circle(0,-3,0.12)
)}}} Graph of {{{3x+4y=-12}}}