Question 171788
Do you want to graph this?



{{{8x+9y=11}}} Start with the given equation.



{{{9y=11-8x}}} Subtract {{{8x}}} from both sides.



{{{9y=-8x+11}}} Rearrange the terms.



{{{y=(-8x+11)/(9)}}} Divide both sides by {{{9}}} to isolate y.



{{{y=((-8)/(9))x+(11)/(9)}}} Break up the fraction.



{{{y=-(8/9)x+11/9}}} Reduce.






In order to graph the equation {{{y=-(8/9)x+11/9}}}, we only need two points to create a straight line





--------------------------------Let's find the first point--------------------------------


{{{y=-(8/9)x+11/9}}} Start with the given equation



{{{y=-(8/9)(7)+11/9}}} Plug in {{{x=7}}} 



{{{y=-56/9+11/9}}} Multiply {{{-8/9}}} and {{{7}}} to get {{{-56/9}}}



{{{y=-45/9}}} Add  



{{{y=-5}}} Reduce



So when {{{x=7}}}, we have the value {{{y=-5}}}. This means we have the first point *[Tex \LARGE \left(7,-5\right)]





--------------------------------Let's find the second point--------------------------------


{{{y=-(8/9)x+11/9}}} Start with the given equation



{{{y=-(8/9)(-2)+11/9}}} Plug in {{{x=-2}}} 



{{{y=16/9+11/9}}} Multiply {{{-8/9}}} and {{{-2}}} to get {{{16/9}}}



{{{y=27/9}}} Add  



{{{y=3}}} Reduce




So when {{{x=-2}}}, we have the value {{{y=3}}}. This means we have the second point *[Tex \LARGE \left(-2,3\right)]





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



So we have the two points: *[Tex \LARGE \left(7,-5\right)] and *[Tex \LARGE \left(-2,3\right)]



Now plot these two points on a coordinate system


{{{drawing(500,500,-7.5,12.5,-7.5,12.5,
graph(500,500,-7.5,12.5,-7.5,12.5,0),
grid(1),
circle(7,-45/9,0.1),
circle(7,-45/9,0.12),
circle(7,-45/9,0.15),
circle(-2,27/9,0.1),
circle(-2,27/9,0.12),
circle(-2,27/9,0.15)
) }}}




Now draw a straight line through the two points. This line is the graph of {{{y=-(8/9)x+11/9}}}


{{{drawing(500,500,-7.5,12.5,-7.5,12.5,
graph(500,500,-7.5,12.5,-7.5,12.5,-(8/9)x+11/9),
grid(1),
circle(7,-45/9,0.1),
circle(7,-45/9,0.12),
circle(7,-45/9,0.15),
circle(-2,27/9,0.1),
circle(-2,27/9,0.12),
circle(-2,27/9,0.15)
) }}} Graph of {{{y=-(8/9)x+11/9}}} through the two points *[Tex \LARGE \left(7,-5\right)] and *[Tex \LARGE \left(-2,3\right)]