Question 201871

<h4>x-intercept</h4>

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



{{{4x-6y = -24}}} Start with the given equation.



{{{4x-6(0) = -24}}} Plug in {{{y=0}}}.



{{{4x-0 = -24}}} Multiply {{{-6}}} and 0 to get 0.



{{{4x = -24}}} Simplify.



{{{x=(-24)/(4)}}} Divide both sides by {{{4}}} 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



{{{4x-6y = -24}}} Start with the given equation.



{{{4(0)-6y = -24}}} Plug in {{{x=0}}}.



{{{0-6y = -24}}} Multiply {{{4}}} and 0 to get 0.



{{{-6y = -24}}} Simplify.



{{{y=(-24)/(-6)}}} Divide both sides by {{{-6}}} 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-6y = -24}}}, we can see that the graph has the x-intercept *[Tex \LARGE \left(-6,0\right)] and the y-intercept *[Tex \LARGE \left(0,4\right)]


{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(-24-4x)/(-6))

)}}} Graph of {{{4x-6y = -24}}}