co-ordinate geometry .

[Md.Nazrul Islam]

If line K in the xy-plane has equation y= mx+b, where m and b are constant .what is the slope of line K.

1)K is parallel to the line with equation y=(1-m)x+b+1.

2)K intersect the line with equation y=2x+3 at the point (2,7).

[Anurag@Gurome]

If line K in the xy-plane has equation y= mx+b, where m and b are constant .what is the slope of line K.

1)K is parallel to the line with equation y=(1-m)x+b+1.

2)K intersect the line with equation y=2x+3 at the point (2,7).

We have to find the value of m.

(1) K is parallel to the line with equation y = (1 - m)x + (b + 1) implies slope of line K = (1 - m) as parallel lines have same slope.
So, m = 1 - m
2m = 1
m = 1/2; SUFFICIENT.

(2) K intersect the line with equation y = 2x + 3 at the point (2, 7) means (2, 7) lies on y = mx + b.
So, (2, 7) on y = mx + b implies 7 = 2m + b but we cannot find m from here; NOT sufficient.

The correct answer is A.