Question 333721


<h4>x-intercept</h4>

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



{{{2x+4y=16}}} Start with the given equation.



{{{2x+4(0)=16}}} Plug in {{{y=0}}}.



{{{2x+0=16}}} Multiply {{{4}}} and 0 to get 0.



{{{2x=16}}} Simplify.



{{{x=(16)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=8}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(8,0\right)].



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<h4>y-intercept</h4>

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



{{{2x+4y=16}}} Start with the given equation.



{{{2(0)+4y=16}}} Plug in {{{x=0}}}.



{{{0+4y=16}}} Multiply {{{2}}} and 0 to get 0.



{{{4y=16}}} Simplify.



{{{y=(16)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



{{{y=4}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,4\right)].



Now let's plot the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(0,4\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0)
circle(8,0,0.03),circle(8,0,0.05),circle(8,0,0.08),circle(8,0,0.10),circle(8,0,0.12),
circle(0,4,0.03),circle(0,4,0.05),circle(0,4,0.08),circle(0,4,0.10),circle(0,4,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{2x+4y=16}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(16-2x)/(4)),
circle(8,0,0.03),circle(8,0,0.05),circle(8,0,0.08),circle(8,0,0.10),circle(8,0,0.12),
circle(0,4,0.03),circle(0,4,0.05),circle(0,4,0.08),circle(0,4,0.10),circle(0,4,0.12)
)}}} Graph of {{{2x+4y=16}}}