Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.
The underlined part is what i could not get.
1. The pair of parallel lines have the common slope $\displaystyle m = \frac32$.
2. $\displaystyle ax-(a+1)y+2=0~\implies~y=\dfrac{a}{a+1} \cdot x + \dfrac2{a+1}$
3. If the line in question doesn't intersect the two parallels it must be parallel to both, that means it's slope must be $\displaystyle m = \frac32$ too. Therefore:
$\displaystyle \dfrac{a}{a+1}=\dfrac32~\implies~2a=3a+3~\implies~ a=-3$
EDIT: @ArchieMeade: Thanks!