# Question

Is there an easier way to solve problems such as this?

I mean we know that quadrants have their respective x, y properties, Q1 +x,+y, Q2 -x,+y, etc.

Is there a counterpart for determining such in a slope?

Say for instance m = 2/3 will never pass Q4. In general, if slope is positive, it never passes Q4. Similarly, if slope is negative, it never passes Q3. Is this true?

# Answer

Yes, that's definitely an easier way to solve this. If a line has a *positive slope* AND a *positive y-intercept*, then it will never pass through Q4. You can come up with similar rules for each combination:

- positive slope, negative y-intercept - never pass through Q2
- negative slope, positive y-intercept - never pass through Q3
- negative slope, negative y-intercept - never pass through Q1

We can also state these rules:

- positive slope - will always pass through Q1 and Q3
- negative slope - will always pass through Q2 and Q4

From Statement 2, we know that the slope is positive. Therefore, we know that it will pass through Q3, so it is sufficient.

# Link

http://gmat.magoosh.com/questions/1028

## Comments