Question 164588
Do you want to find the x and y intercepts?




<h4>x-intercept</h4>

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



{{{2x-3y=-12}}} Start with the given equation.



{{{2x-3(0)=-12}}} Plug in {{{y=0}}}.



{{{2x-0=-12}}} Multiply {{{-3}}} and 0 to get 0.



{{{2x=-12}}} Simplify.



{{{x=(-12)/(2)}}} Divide both sides by {{{2}}} 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



{{{2x-3y=-12}}} Start with the given equation.



{{{2(0)-3y=-12}}} Plug in {{{x=0}}}.



{{{0-3y=-12}}} Multiply {{{2}}} 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 {{{2x-3y=-12}}} (you have to solve for y first), 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,
grid(0),
graph(500, 500, -10, 10, -10, 10,(-12-2x)/(-3))
)}}} Graph of {{{2x-3y=-12}}}