DETERMINE whether the 2 lines are parallel, perpendicular, or neither.

9x+2y=-10

y=-9/2x-6

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- Jul 2nd 2009, 11:28 AMInsignia21Help
DETERMINE whether the 2 lines are parallel, perpendicular, or neither.

9x+2y=-10

y=-9/2x-6 - Jul 2nd 2009, 01:09 PMKasper
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 PMHallsofIvy
Well done, Kaspar!

**Up to**this point!

Quote:

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

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

**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 PMKasper
Oh dear. Wow. Thanks for that clarification!