Quadrants

The xy-plane is divided into four quadrants.  While the SAT often gives a picture showing the quadrants, you may see a problem where you need to have them memorized.

An example:

If the equation \(y=-2x+3\) is graphed in the xy-plane, which quadrant will have no solutions?

A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants

Strategy:

  1. Get whatever lines or inequalities you’re given into \(y=mx+b\)
  2. If a quadrant plane is given (pictured above), draw the lines or inequalities on the plane.
  3. If there is no quadrant plane given, draw your own, then draw the lines or inequalities onto it.

Another example:

Line j in the xy-plane contains points from quadrants II and III, but no points from quadrants I or IV.  Which of the following must be true about line j ?

A) The slope is undefined
B) The slope is zero
C) The slope is positive
D) The slope is negative

For a line to never cross the y axis, it would have to be a straight vertical line – remember slope is rise over run, and if there is no run we will be dividing by 0.  The answer is A).