# Help

• Jul 2nd 2009, 11:28 AM
Insignia21
Help
DETERMINE whether the 2 lines are parallel, perpendicular, or neither.

9x+2y=-10

y=-9/2x-6
• Jul 2nd 2009, 01:09 PM
Kasper
Quote:

Originally Posted by Insignia21
DETERMINE whether the 2 lines are parallel, perpendicular, or neither.

1) $\displaystyle 9x+2y=-10$

2) $\displaystyle y=-\frac{9}{2}x-6$

Hey Insignia21,

A good piece of information to know here is that if 2 lines are parallel, they will have the same slope, and if they are perpendicular, the slopes will be negative reciprocals of one another.That said, we can see clearly the the slope of $\displaystyle y=-\frac{9}{2}x-6$ is $\displaystyle m=-\frac{9}{2}$. We know this from knowing the formula for a straight line $\displaystyle y=mx+b$ where $\displaystyle m=slope$

So we know that for $\displaystyle 9x+2y=-10$ to be parallel, it must have a slope of $\displaystyle m=-\frac{9}{2}$, and if it is perpendicular, it must have a slope of $\displaystyle m=\frac{2}{9}$.

Now we must solve the first equation for y and find the slope, and then compare it to the above.

$\displaystyle 9x+2y=-10$

$\displaystyle 2y=-10-9x$
$\displaystyle y=-5-\frac{9}{5}x$
$\displaystyle y=-\frac{9}{5}x-5$

And from this we can see that the slope of
$\displaystyle 9x+2y=-10$ is $\displaystyle m=\frac{9}{5}$ which when compared above is not the same or the negative reciprocal of the second equation. Therefore the 2 lines are neither parallel or perpendicular.

Does this help?
• Jul 2nd 2009, 05:18 PM
HallsofIvy
Quote:

Originally Posted by Kasper
Hey Insignia21,

A good piece of information to know here is that if 2 lines are parallel, they will have the same slope, and if they are perpendicular, the slopes will be negative reciprocals of one another.That said, we can see clearly the the slope of $\displaystyle y=-\frac{9}{2}x-6$ is $\displaystyle m=-\frac{9}{2}$. We know this from knowing the formula for a straight line $\displaystyle y=mx+b$ where $\displaystyle m=slope$

So we know that for $\displaystyle 9x+2y=-10$ to be parallel, it must have a slope of $\displaystyle m=-\frac{9}{2}$, and if it is perpendicular, it must have a slope of $\displaystyle m=\frac{2}{9}$.

Now we must solve the first equation for y and find the slope, and then compare it to the above.

$\displaystyle 9x+2y=-10$

$\displaystyle 2y=-10-9x$

Well done, Kaspar! Up to this point!

Quote:

$\displaystyle y=-5-\frac{9}{5}x$
$\displaystyle y=-\frac{9}{5}x-5$
No, you divide both sides by 2 so this is
$\displaystyle y= -\frac{9}{2}x- 5$
and the slopes are the same!

Quote:

And from this we can see that the slope of
$\displaystyle 9x+2y=-10$ is $\displaystyle m=\frac{9}{5}$ which when compared above is not the same or the negative reciprocal of the second equation. Therefore the 2 lines are neither parallel or perpendicular.

Does this help?
• Jul 2nd 2009, 05:20 PM
Kasper
Oh dear. Wow. Thanks for that clarification!