Question

Which of the following statements is not always correct?

• A. x – 3 = 0, is the equation of a line parallel to the y-axis and passing through (3, 0).
• B. The equation y = 4x + 3b, where b is a constant, has infinitely many solutions.
• C. The equation of line whose x-coordinate is always thrice of the y-coordinate is x = 3y.
• D. The graph of the equation y = mx + c always passes through the origin.

Answer 1

The correct option is D The graph of the equation y = mx + c always passes through the origin.

The equation x = k is a line parallel to y-axis and passes through (k, 0), where k is a real number.
Thus, x – 3 = 0, i.e., x = 3 is a line parallel to y-axis, passing through (3, 0).
A linear equation in two variables has infinitely many solutions, therefore, the equations y = 4x + 3b has infinite solutions.
The equation of the line whose x-coordinate is always thrice of y-coordinate is given as x = 3y.
The graph of the equation y = mx + c will pass through the origin only when c = 0.
Thus, y = mx + c does not pass through the origin always. Hence, the correct answer is option (d).