Question 316122

<h4>x-intercept</h4>

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



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



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



{{{2x = 4 }}} Simplify.



{{{x=(4)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



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



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<h4>y-intercept</h4>

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



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



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



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



{{{ y = 4 }}} Simplify.



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



Now let's plot the points *[Tex \LARGE \left(2,0\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(2,0,0.03),circle(2,0,0.05),circle(2,0,0.08),circle(2,0,0.10),circle(2,0,0.12),
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 + y = 4 }}}.



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