Question 309896

<h4>x-intercept</h4>

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



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



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



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



{{{x=8}}} Simplify.



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



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



{{{0 + 4y = 8}}} Plug in {{{x=0}}}.



{{{4y = 8}}} Simplify.



{{{y=(8)/(4)}}} Divide both sides by {{{4}}} 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(8,0\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(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(0,2,0.03),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 {{{x + 4y = 8}}}.



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