Question

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

Answer 1

Answer:

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

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