Question

A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The given line is 3x + y = 3 …… (1)

The slope of line (1) is –3

$\therefore$ Slope of the line which is perpendicular to line (1) is $\frac{1}{3}$

Now, equation of the line through the point (2, 2) and perpendicular to line (1) is (y – 2) = $\frac{1}{3}$ (x – 2)

$\Rightarrow$ 3y – 6 = x – 2

$\Rightarrow$ x – 3y + 4 = 0 …… (2)

Its y-intercept $=\frac{4}{3}$ . [Putting x = 0 in (2)]