# Math Help - Coordinate geometry--

1. ## Coordinate 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.

2. ## rewrite

Originally Posted by Ilsa
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.
well this is a try at it...rewrite
$2y-3x=4$ as $y=\frac{3}{2}x+2$
Then at $(5,2)$ the eq is $y=\frac{3}{2}x-\frac{11}{2}$

3. ## correction

Originally Posted by Ilsa
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 $m = \frac32$.

2. $ax-(a+1)y+2=0~\implies~y=\dfrac{a}{a+1} \cdot x + \dfrac2{a+1}$

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 $m = \frac32$ too. Therefore:

$\dfrac{a}{a+1}=\dfrac32~\implies~2a=3a+3~\implies~ a=-3$

Hence $a=-3$