Question

Which of these lines pass through the point (3, 2)?

• A. $2x-3y=2$
• B. $3x-2y=2$
• C. $3x-2y=0$
• D. $2x-3y=0$

Answer 1

The correct option is D $2x-3y=0$

A line passes through a point if the coordinates of the point satisfy the equation of the line.
Substituting the point (3, 2) in

1) 2x - 3y = 2 we get,
RHS = 2 and RHS = 2(3) - 3(2) = 0 $\ne$ 2
Thus, LHS $\ne$ RHS and the line 2x - 3y =2 does not passes through the point (3, 2).

2) 3x - 2y = 2 we get,
RHS = 2 and LHS = 3(3) - 2(2) = 5 $\ne$ 2
Thus LHS $\ne$ RHS and the line 3x - 2y = 2 does not pass through the point (3, 2).

3) 3x - 2y = 0 we get,
RHS = 0 and LHS = 3(3) - 2(2) = 5 $\ne$ 0
Thus, LHS $\ne$ RHS and the line 3x - 2y = 0 does not passes through the point (3, 2).

4) 2x - 3y = 0 we get,
RHS = 0 and LHS = = 2(3) - 3(2) = 0
Thus, LHS = RHS and the line 2x - 3y = 0 passes through the point (3, 2)