Question

Which of these lines do not pass through the point (2, 2)?

• A. y = 3x - 4
• B. 2x = y - 6
• C. y = 4 - x
• D. 3y - 2x = 2

Answer 1

The correct option is B

2x = y - 6

A line passes through a point if the coordinates of the point satisfy the equation of the line.

Substituting the point (2, 2) in given equations

1) From y = 3x - 4, we get
LHS = 2
RHS = 3(2) - 4 = 6 - 4 = 2
LHS = RHS
Therefore, the line y = 3x - 4 passes through the point (2, 2).

2) From 2x = y - 6, we get
LHS = 2(2) = 4
RHS = 2 - 6 = -4
LHS $\ne$ RHS
Therefore, the line 2x = y - 6 does not pass through the point (2, 2).

3) From y = 4 - x, we get
LHS = 2
RHS = 4 - 2 = 2
LHS = RHS
Therefore, the line y = 4 - x passes through the point (2, 2).

4) From 3y - 2x = 2, we get
LHS = 3(2) - 2(2) = 6 - 4 = 2
RHS = 2
LHS = RHS
Therefore, the line 3y - 2x = 2 passes through the point (2, 2).