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Chapter 1: Problem 76

List the quadrant or quadrants satisfying each condition. $$\frac{y}{x}<0$$

Short Answer

Expert verified
The condition \(\frac{y}{x}<0\) is met in the second and fourth quadrants.

Step by step solution

01

Determine the Sign in Each Quadrant

In each quadrant, the sign of the ratio \(\frac{y}{x}\) depends on the signs of \(x\) and \(y\). To determine this, remember that in the first quadrant, both \(x\) and \(y\) are positive, in the second quadrant \(x\) is negative and \(y\) positive, in the third quadrant both are negative, and in the fourth quadrant \(x\) is positive and \(y\) is negative.
02

Find the Quadrants where the Condition is Met

The ratio will be less than zero (\(\frac{y}{x}<0\)) in the quadrants where \(x\) and \(y\) have different signs. These quadrants are the second and fourth quadrants. In the second quadrant, we have the situation of positive \(y\) over negative \(x\), which results in a negative number. In the fourth quadrant, we have negative \(y\) over positive \(x\), which also results in a negative number.

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