Question 254638


<h4>x-intercept</h4>

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)].



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<h4>y-intercept</h4>

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



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



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



{{{2y=4}}} Simplify.



{{{y=(4)/(2)}}} Divide both sides by {{{2}}} 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, -5, 5, -5, 5,
grid(0),
graph(500, 500, -5, 5, -5, 5,0)
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 {{{x+2y=4}}}.



{{{ drawing(500, 500, -5, 5, -5, 5,
grid(0),
graph(500, 500, -5, 5, -5, 5,(4-x)/(2)),
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 {{{x+2y=4}}}