GMATFocus Q3 - Coordinate Geometry

[frizo]

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

A

[x2suresh]

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.

[frizo]

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

[BuckeyeT]

(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.

[bluementor]

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-

[bhumika.k.shah]

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.

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-

[stufigol]

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