Question 157950

<h4>x-intercept</h4>

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



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



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



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



{{{-6=2x}}} Combine like terms.



{{{-3=x}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



So the answer is {{{x=-3}}} 



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



------------------------------------------



<h4>y-intercept</h4>

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



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



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



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



{{{2y=6}}} Add {{{6}}} to both sides.



{{{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)].





So we have these intercepts:

x-intercept: *[Tex \Large \left(-3,0\right)]


y-intercept: *[Tex \Large \left(0,3\right)]




Now plot the two points *[Tex \Large \left(-3,0\right)] and *[Tex \Large \left(0,3\right)] 


{{{drawing(500, 500, -7, 7, -7, 7,
graph(500, 500, -7, 7, -7, 7,0),
circle(-3,0,0.0666666666666667),
circle(-3,0,0.0966666666666667),

circle(0,3,0.0666666666666667),
circle(0,3,0.0966666666666667)


)}}}



Now draw a line through the two points to graph {{{-2*x+2*y=6}}}

{{{drawing(500, 500, -7, 7, -7, 7,
graph(500, 500, -7, 7, -7, 7,(6--2*x)/2),
circle(-3,0,0.0666666666666667),
circle(-3,0,0.0966666666666667),

circle(0,3,0.0666666666666667),
circle(0,3,0.0966666666666667)


)}}} graph of {{{-2*x+2*y=6}}} through the x-intercept*[Tex \Large \left(-3,0\right)] and y-intercept *[Tex \Large \left(0,3\right)]