Question

Graph of the equation ax+by+c=0 , a≠0, b≠0, cuts x axis and y axis respectively at points

a. (-c/a,0).(0,-c/b)
b. (0,-c/b).(-c/b,0)
c. (-c,0).(0,-c)
d. (-c,0).(0,-c)

Answer 1

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.