Question 206009
The goal here is to first get the standard equation {{{Ax+By=C}}} into the slope-intercept equation {{{y=mx+b}}}



{{{(2+k)x + (2-k)y = 15}}} Start with the given equation.



{{{(2-k)y = 15-(2+k)x}}} Subtract {{{(2+k)x}}} from both sides.



{{{(2-k)y = -(2+k)x+15}}} Rearrange the terms.



{{{y = (-(2+k)x+15)/(2-k)}}} Divide both sides by {{{2-k}}} to isolate "y".



{{{y = -((2+k)/(2-k))x+15/(2-k)}}} Break up the fraction



Now the equation is in the form {{{y=mx+b}}} where the slope is {{{m=-(2+k)/(2-k)}}} and the y-intercept is {{{b=15/(2-k)}}}



Because we want the slope to be {{{3/2}}}, this means that {{{m=3/2}}}



So the next step is to solve {{{3/2=-(2+k)/(2-k)}}} for 'k'. I'll let you do that.