XY-Plane has equation

[abhi332]

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)

[ldoolitt]

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)

Its obvious that (1) is sufficient. By geometry rules you know that parallel lines share a slope. Thus you can set the two slopes to equate:

1-m = m
2m = 1
m = 1/2

For (2) all that really tells you is that point (2,7) is on the line y=mx+b. Since (2) doesnt give you any information about the parallel or perpendicular nature of line K with the current line (although you know they ARENT parallel because they intersect) it doesnt give you enough to answer the question.

Go with (a)

[ajith]

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)

1) 1-m = m

m =1/2 ; sufficient

2) y = mx+b passes through 2,7
7= 2m+b

there are different values of m which will satisfy this; insufficient

A