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Questions  >>  CBSE XI  >>  Math  >>  Straight Lines
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Q)

Choose the correct answer from the given four options. A line passes through (2, 2) and is perpendicular to the line $3x + y=3$. Its y - intercept is

$\begin {array} {1 1} (A)\;\large\frac{1}{3} & \quad (B)\;\large\frac{2}{3} \\ (C)\;1 & \quad (D)\;\large\frac{4}{3} \end {array}$

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A)
Toolbox:
  • Slope of a line which is perpendicular to a line having slope 'm' is $ - \large\frac{1}{m}$.
  • Equation of a line having slope $m$ and passing through $(x_1, y_1)$ is $ (y-y_1)=m(x-x_1)$
Step 1 :
Equation of the given line is $ - \large\frac{3}{1}$$ = -3$
Hence slope of the line which is perpendicular to the above line is $ \large\frac{1}{3}$
It is given that the line passes through the point (2,2)
Hence equation of the required line is $(y-2)=\large\frac{1}{3}$$(x-2)$
$ \Rightarrow 3y-6=x-2$
(i.e) $3y=x+4$
$ \therefore y = \large\frac{1}{3}$$x+ \large\frac{4}{3}$
Hence the y intercept is $ \large\frac{4}{3}$
Hence 'D' is the correct option.
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