frizo wrote:If Line K in th 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-x)x + b + 1
2) K intersects the line with equation y=2x+3 at the point (2,7))

A

y = (1-x)x + b + 1
--> is not a line.. looks lit it is parabola.. Please check the question again.

Sorry, it is y = (1-m)x + b + 1

(1) If K is parallel to another line, they share the same slope. Since (1) states the line y=(1-m)x + b + 1, it is of the form y = mx + b (where m=slope, b=y-intercept). So, we know the slope is (1-m) and the intercept is (b + 1) where m and b are constants. Since we can state the answer as a constant value (slope of k = (1-m)), the statement is sufficient.

(2) This statement gives us the intercept of the two lines and the slope of 1 line. The other line can have a variety of slopes other than the slope given and still intersect at (2,7) - try drawing a line on paper, pick a point on that paper, and see how many lines you can draw through that line. This statement is insufficient.

So, A.

If two straight lines are parallel, then they have the same slopes.

Statement 1: Lines y=mx+b and y=(1-m)x+b+1 are parallel, therefore:

m = 1-m
m=0.5 , Sufficient.

Statement 2: A line that intersects y=2x+3 at (2,7) can have any slope, therefore insufficient.

Choose A.

-BM-

This looks simple But what about that +1 in the equation y=(1-m)x+b+1

Are we to ignore that ? if so, then why ? If we consider it , then the answer would change.

bluementor wrote:If two straight lines are parallel, then they have the same slopes.

Statement 1: Lines y=mx+b and y=(1-m)x+b+1 are parallel, therefore:

m = 1-m
m=0.5 , Sufficient.

Statement 2: A line that intersects y=2x+3 at (2,7) can have any slope, therefore insufficient.

Choose A.

-BM-

you don t have to consider it...
it is like y= (1-m)x+ D with D=b+1
U just need to consider that they are parallel not the distance between the two...if u change D they ll still be // but the distance will change