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.

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- Oct 19th 2010, 08:52 AMIlsaCoordinate geometry--
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. - Oct 19th 2010, 08:01 PMbigwaverewrite
- Oct 19th 2010, 10:57 PMearbothcorrection
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! - Oct 20th 2010, 02:14 PMArchie Meade
The slopes of all 3 lines must be equal.

Hence $\displaystyle a=-3$