Question 171368
I'll do two of each to give you examples to work with



# 1




<h4>x-intercept</h4>


The x-intercept occurs when {{{y=0}}} (graphically this is on the x-axis).



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



{{{x-2y=4}}} Start with the given equation.



{{{x-2(0)=4}}} Plug in {{{y=0}}}.



{{{x-0=4}}} Multiply {{{-2}}} and 0 to get 0.



{{{x=4}}} Simplify.



So the x-intercept is *[Tex \LARGE \left(4,0\right)]. Note: the x-intercept is in the form (some number, 0)



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# 2



{{{2x-3y=6}}} Start with the given equation.



{{{2x-3(0)=6}}} Plug in {{{y=0}}}.



{{{2x-0=6}}} Multiply {{{-3}}} and 0 to get 0.



{{{2x=6}}} Simplify.



{{{x=(6)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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



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# 6




<h4>y-intercept</h4>


The y-intercept occurs when {{{x=0}}} (notice how the opposite is the case for the x-intercept).



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



{{{y=-3x+7}}} Start with the given equation.



{{{y=-3(0)+7}}} Plug in {{{x=0}}}.



{{{y=0+7}}} Multiply {{{-3}}} and {{{0}}} to get {{{0}}}.



{{{y=7}}} Combine like terms.



So the y-intercept is *[Tex \LARGE \left(0,7\right)]. Note: the y-intercept is in the form (0, some number)




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# 7



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



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



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



{{{y=-24}}} Combine like terms.



So the y-intercept is *[Tex \LARGE \left(0,-24\right)].



Note: you can see if the equation is in the form {{{y=mx+b}}}, then the y-intercept is simply (0,b). So we can avoid the work in problems #6, and #7 by just looking at the last value.