<PRE><B>Question 178964</B>
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point (3, -6) and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point (7, y)



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula 


{{{7=(y-(-6))/(7-3)}}} Plug in {{{m=7}}} (the given slope) {{{y[2]=y}}}, {{{y[1]=-6}}}, {{{x[2]=7}}}, and {{{x[1]=3}}} (the coordinates of the given points)



{{{7=(y+6)/(7-3)}}} Rewrite {{{y-(-6)}}} as {{{y+6}}}



{{{7=(y+6)/(4)}}} Subtract



{{{7*4=y+6}}} Multiply both sides by 4



{{{28=y+6}}} Multiply



{{{28-6=y}}} Subtract 6 from both sides.



{{{22=y}}} Combine like terms.



So the answer is {{{y=22}}}</PRE>