<PRE><B>Question 157860</B>


&lt;h4&gt;x-intercept&lt;/h4&gt;

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{4x+3y=12}}} Start with the given equation.



{{{4x+3(0)=12}}} Plug in {{{y=0}}}.



{{{4x+0=12}}} Multiply {{{3}}} and 0 to get 0.



{{{4x=12}}} Simplify.



{{{x=(12)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(3,0\right)].



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&lt;h4&gt;y-intercept&lt;/h4&gt;

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{4x+3y=12}}} Start with the given equation.



{{{4(0)+3y=12}}} Plug in {{{x=0}}}.



{{{0+3y=12}}} Multiply {{{4}}} and 0 to get 0.



{{{3y=12}}} Simplify.



{{{y=(12)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



{{{y=4}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,4\right)].



Notice that if we graph the equation {{{4x+3y=12}}}, we can see that the graph has the x-intercept *[Tex \LARGE \left(3,0\right)] and the y-intercept *[Tex \LARGE \left(0,4\right)]. So this verifies our answer.



{{{ drawing(500, 500, -5, 5, -5, 5,
grid(0),
graph(500, 500, -5, 5, -5, 5,(12-4x)/(3))
)}}} Graph of {{{4x+3y=12}}}
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