Question

The lines 2x – 5 = ky and (k + 1)x = 6y - 3 have the same gradient. Find the possible values of k.​

Answer 1

Answer:

2x−k=ky

2x−k=ky

(k+1)x=6y−3

(k+1)x=6y−3

Change it to this form!

y=mx+c

y=mx+c

y=2xk−1

y=2xk−1

y=(k+1)x6+12

y=(k+1)x6+12

Since their gradient is the same then

2k=k+16

2k=k+16

12=k2+k

12=k2+k

k2+k−12=0

k2+k−12=0

(k+4)(k−3)=0

(k+4)(k−3)=0

k=−4

k=−4

k=3

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