Question

The lines 2x=ky+2 and (k+1)x=6y-3 have same gradient. Find possible values of k

I need the answers ASAP please!

Answer 1

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Explanation:

`2x=ky+2\to\ eq1\\(k+1)x=6y-3\to\ eq2\\$Change to this form: $y=mx+c\\ky=2x-2\\y=(2x-2)/(k)\\$gradient of eq1: $(2)/(k)\\6y=(k+1)x+3\\y=((k+1)x+3)/(6)\\y=(k+1)/(6) x+(3)/(6)\\y= (k+1)/(6) x+(1)/(2)\\$gradient of eq1: $(k+1)/(6)\\$Since gradient, m, is the same for both lines,$\\(2)/(k)=(k+1)/(6)\\12=k^(2)+k\\k^(2)+k-12=0\\(k-3)(k+4)=0\\k=3 $ or $ k=-4`