Could anyone answer and also provide explanation.

b

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

2x + 3y = 1 ( subtract 2x from both sides )

3y = - 2x + 1 ( divide all terms by 3 )

y = - x + ← in slope- intercept form

with y- intercept c = ← does not pass through the origin

(b)

2x + 3y = 0 ( subtract 2x from both sides )

3y = - 2x + 0 ( dividing all sides by 3 ), gives

y = - x + 0 ← in slope- intercept form

with y- intercept c = 0 ← passes through the origin

(c)

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide all terms by 3 )

y = - x + 2

with y- intercept c = 2 ← does not pass through the origin

answer: do you still need this?