Question 777736
Assuming the equation is 3x+2y = 6




<h4>x-intercept</h4>

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



{{{3x+2y=6}}} Start with the given equation.



{{{3x+2(0)=6}}} Plug in {{{y=0}}}.



{{{3x+0=6}}} Multiply {{{2}}} and 0 to get 0.



{{{3x=6}}} Simplify.



{{{x=(6)/(3)}}} Divide both sides by {{{3}}} 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



{{{3x+2y=6}}} Start with the given equation.



{{{3(0)+2y=6}}} Plug in {{{x=0}}}.



{{{0+2y=6}}} Multiply {{{3}}} and 0 to get 0.



{{{2y=6}}} Simplify.



{{{y=(6)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



{{{y=3}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,3\right)].



Now let's plot the points *[Tex \LARGE \left(2,0\right)] and *[Tex \LARGE \left(0,3\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(0,3,0.03),circle(0,3,0.05),circle(0,3,0.08),circle(0,3,0.10),circle(0,3,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{3x+2y=6}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(6-3x)/(2)),
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(0,3,0.03),circle(0,3,0.05),circle(0,3,0.08),circle(0,3,0.10),circle(0,3,0.12)
)}}} Graph of {{{3x+2y=6}}}