Concept:The line passes through the intersection point of two given lines and makes equal intercepts with the axes in the fourth quadrant.
Explanation:First, find the intersection of
x+2y+2=0 and
2x−3y−3=0.
From the first equation:
x=−2y−2. Substitute into the second:
2(−2y−2)−3y−3=0 →
−4y−4−3y−3=0 →
−7y−7=0 →
y=−1. Then
x=−2(−1)−2=0. So the intersection point is
(0,−1).
Since the line cuts equal intercepts in the fourth quadrant, let the x‑intercept be
a (positive) and the y‑intercept be
−a (negative, because the fourth quadrant has positive x and negative y). The intercept form of the line is
ax​+−ay​=1, which simplifies to
x−y=a.
The line passes through
(0,−1). Substitute:
0−(−1)=a →
a=1. Hence the intercepts are
1 on the x‑axis and
−1 on the y‑axis. Their absolute values are
1 and
1. The sum of absolute values is
1+1=2.
Answer:2 (Option A)