The correct answer is option a. (-c/a 0) and (0 -c/b).
To understand why let's consider the equation ax + by + c = 0.
To find the point where the equation intersects the x-axis we set y = 0 and solve for x:
ax + by + c = 0
ax + 0 + c = 0
ax + c = 0
ax = -c
x = -c/a
Therefore the equation intersects the x-axis at the point (-c/a 0).
To find the point where the equation intersects the y-axis we set x = 0 and solve for y:
ax + by + c = 0
0 + by + c = 0
by + c = 0
by = -c
y = -c/b
Therefore the equation intersects the y-axis at the point (0 -c/b).
Hence option a. (-c/a 0) and (0 -c/b) is the correct answer.