Question

In the rectangular quadrant system shown above, which quadrant, if any, contains no point \( (x, y) \) that satisfies the equation \( 3x + 5y = -2 \)?

• A. none
• B. I
• C. II
• D. III
• E. IV

Hint:

To determine if an equation satisfies a quadrant, plot the intercepts and analyze which quadrants are intersected by the line.

Answer 1

The Correct Option is A

Step 1: Write the equation of the line.
The given equation is \( 3x + 5y = -2 \). To find the intercepts:
- For \( x \)-intercept: Set \( y = 0 \), then \( 3x = -2 \Rightarrow x = -\frac{2}{3} \).
- For \( y \)-intercept: Set \( x = 0 \), then \( 5y = -2 \Rightarrow y = -\frac{2}{5} \).
Step 2: Plot the points.
The intercepts are \( (-\frac{2}{3}, 0) \) and \( (0, -\frac{2}{5}) \). These points lie in the negative half of both axes.
Step 3: Analyze the quadrants.
The line passes through Quadrants II and III, and no quadrant is void of points satisfying the equation. Thus, the correct answer is (A) none.