Question 385261


<h4>x-intercept</h4>

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



{{{-4x+8y=-16}}} Start with the given equation.



{{{-4x+8(0)=-16}}} Plug in {{{y=0}}}.



{{{-4x+0=-16}}} Multiply {{{8}}} and 0 to get 0.



{{{-4x=-16}}} Simplify.



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



{{{x=4}}} Reduce.



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



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<h4>y-intercept</h4>

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



{{{-4x+8y=-16}}} Start with the given equation.



{{{-4(0)+8y=-16}}} Plug in {{{x=0}}}.



{{{-0+8y=-16}}} Multiply {{{-4}}} and 0 to get 0.



{{{8y=-16}}} Simplify.



{{{y=(-16)/(8)}}} Divide both sides by {{{8}}} to isolate {{{y}}}.



{{{y=-2}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-2\right)].



Now let's plot the points *[Tex \LARGE \left(4,0\right)] and *[Tex \LARGE \left(0,-2\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(4,0,0.03),circle(4,0,0.05),circle(4,0,0.08),circle(4,0,0.10),circle(4,0,0.12),
circle(0,-2,0.03),circle(0,-2,0.05),circle(0,-2,0.08),circle(0,-2,0.10),circle(0,-2,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{-4x+8y=-16}}}.



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



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Jim