Question 173087


First let's find the slope of the line through the points *[Tex \LARGE \left(0,-1\right)] and *[Tex \LARGE \left(8,8\right)]



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(8--1)/(8-0)}}} Plug in {{{y[2]=8}}}, {{{y[1]=-1}}}, {{{x[2]=8}}}, and {{{x[1]=0}}}



{{{m=(9)/(8-0)}}} Subtract {{{-1}}} from {{{8}}} to get {{{9}}}



{{{m=(9)/(8)}}} Subtract {{{0}}} from {{{8}}} to get {{{8}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(0,-1\right)] and *[Tex \LARGE \left(8,8\right)] is {{{m=9/8}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y--1=(9/8)(x-0)}}} Plug in {{{m=9/8}}}, {{{x[1]=0}}}, and {{{y[1]=-1}}}



{{{y+1=(9/8)(x-0)}}} Rewrite {{{y--1}}} as {{{y+1}}}



{{{y+1=(9/8)x-(9/8)(0)}}} Distribute



{{{y+1=(9/8)x-0}}} Multiply



{{{y+1=(9/8)x}}} Simplify



{{{y-(9/8)x=-1}}} Subtract {{{(9/8)x}}} from both sides. Subtract 1 from both sides.



{{{-(9/8)x+y=-1}}} Rearrange the terms. 



{{{-9x+8y=-8}}} Multiply EVERY term by the LCD 8 to clear the fraction.



{{{9x-8y=8}}} Multiply EVERY term by -1 to make the "x" coefficient positive.



So now the equation is in standard form {{{Ax+By=C}}} where {{{A=9}}}, {{{B=-8}}}, and {{{C=8}}}