Whenever I see a similar question, my mind freezes and I go into fetal position. I am unable to picture them and even if sketch them, I am still confused as to how approach them.

I know how to get a slope.

I know the basic equation of a line.

I know how a prep bisector works.

I know the distance between two points.

I know how to get the mid between two points.

I am just unable to lump all these together and solve these questions quick enough.

Here are some examples of these questions:

In the xy-plane, if line k has negative slope and passes through the point (−5,r ), is the x-intercept of line k positive?

(1) The slope of line k is –5.

(2) r > 0

Official answer for this one is :

In the rectangular coordinate system, are the points

(r,s) and (u,v ) equidistant from the origin?

(1) r + s = 1

(2) u = 1 – r and v = 1 – s

OA:

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).

OA :

In the XY plane, region R consists of all the points (x,y) such that 2x+3y<=6. Is the point (r,s) in region R?

1. 3r+2s=6

2. r<=3 & s<=2

OA :

These questions seem to pop up on every GMAT prep I took.

Any helps or tricks are appreciated. If I can't thank you in a post, I will make sure I kudos you.