Question 585365
<h4>x-intercept</h4>

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



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



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



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



{{{x=12}}} Simplify.



So the x-intercept is *[Tex \LARGE \left(12,0\right)].



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<h4>y-intercept</h4>

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



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



{{{0-4y=12}}} Plug in {{{x=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(12,0\right)] and *[Tex \LARGE \left(0,-3\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -6,14,-10,10,
grid(0),
graph(500, 500, -6,14,-10,10,0)
circle(12,0,0.03),circle(12,0,0.05),circle(12,0,0.08),circle(12,0,0.10),circle(12,0,0.12),
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 {{{x-4y=12}}}.



{{{ drawing(500, 500, -6,14,-10,10,
grid(0),
graph(500, 500, -6,14,-10,10,(12-x)/(-4)),
circle(12,0,0.03),circle(12,0,0.05),circle(12,0,0.08),circle(12,0,0.10),circle(12,0,0.12),
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 {{{x-4y=12}}}


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