pappueshwar wrote:If Line K in the XY-Plane has equation y=mx+b, where m and b are constants, what is the slope of K?

1. K is parallel to the line with equation y=(1-m)x+(b+1)
2. K intersects the line with equation y=2x+3 at the point (2,7)

[spoiler]
OA IS A [/spoiler]

Request to explain as to how B is not the correct option

Question: If equation of line K is y = mx + b, then what is the slope of K?

(1) K is parallel to the line with equation y = (1 - m)x + (b + 1)
Slope of given line, y = (1 - m)x + (b + 1) is (1 - m)
Since slope of parallel lines are equal, so 1 - m = m implies m = 1/2; SUFFICIENT.

(2) K intersects the line with equation y = 2x + 3 at the point (2,7).
Since line K passes through the point (2, 7), so this point will satisfy y = mx + b
So, 7 = 2m + b but this does help us to find the value of m as there is just one equation and 2 variables; NOT sufficient.

The correct answer is A.