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.
($\displaystyle k \not = 0$)
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,
$\displaystyle k^2=36$
$\displaystyle k=\pm 6$