What positive value of k would make the lines below parallel in the coordinate plane?

9x+ky=16

kx+4y=11

This problem is for extra points.

Printable View

- Dec 7th 2006, 06:50 PMSchatzle06parallel coordinate plane
What positive value of k would make the lines below parallel in the coordinate plane?

9x+ky=16

kx+4y=11

This problem is for extra points. - Dec 7th 2006, 07:43 PMThePerfectHacker
($\displaystyle k \not = 0$)

Express these in slope intercept form,

$\displaystyle ky=-9x+16$

$\displaystyle y=-\frac{9}{k}+\frac{16}{k}$

And,

$\displaystyle 4y=-kx+11$

$\displaystyle y=-\frac{k}{4}x+\frac{11}{4}$

Two (non horizontal non vertical) lines are parralel if and only if there slopes are equal,

$\displaystyle -\frac{k}{4}=-\frac{9}{k}$

Remove the negative from both sides and cross multiply,

$\displaystyle k^2=36$

$\displaystyle k=\pm 6$