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:**

**Get whatever lines or inequalities you’re given into**\(y=mx+b\)**If a quadrant plane is given (pictured above), draw the lines or inequalities on the plane.****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

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).

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