Analytic geometry help please

[coco98]

So im new here and might be doing this wrong but i have test tomorrow and could use some help, by the way im in gr9 so i just need to know how to find the answer but also the answer.

Question: Find the Value(s) of k for which the lines kx-2y-1=0 and8x-ky+3=0 are parallel. Are there any values of k that would make the two lines perpendicular? Explain.

Thanks

 

[DrPhil]

So im new here and might be doing this wrong but i have test tomorrow and could use some help, by the way im in gr9 so i just need to know how to find the answer.

Question: Find the Value(s) of k for which the lines kx-2y-1=0 and8x-ky+3=0 are parallel. Are there any values of k that would make the two lines perpendicular? Explain.

Thank

To be parallel, they have to have the same slope. One of the slopes will have k in the numerator, and the other will have k in the denominator. Set the two slopes equal and solve for k.

For perpendicular, the product of the two slopes = -1. Can you solve the resulting equation for k?

 

[MarkFL]

Suppose you are given the two lines:

$\displaystyle Ax+By+C=0$

$\displaystyle Dx+Ey+F=0$

Now, if we put the lines into slope-intercept form, we have:

$\displaystyle y=-\dfrac{A}{B}x-\dfrac{C}{B}$

$\displaystyle y=-\dfrac{D}{E}x-\dfrac{F}{E}$

Now, you should know that two lines are parallel if their slopes are equal, hence we require:

$\displaystyle \dfrac{A}{B}=\dfrac{D}{E}$

and two lines are perpendicular if the product of their slopes is -1, hence:

$\displaystyle \dfrac{A}{B}=-\dfrac{E}{D}$

So using this, can you proceed?