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KCET2015MathematicsApplication of Derivatives

A line passes through ( (2,2) ) and is perpendicular in the line ( 3 x+y=3 ) its ( y )-intercepts is

Options

  1. A( 1 3 )
  2. B( 2 3 )
  3. C( 4 3 )
  4. D( 11 )

Correct answer

C. ( 4 3 )

Step-by-step solution

Given line, 3 x+y=3 y=-3 x+3 So, slope of this line is m₁=-3 Then, slope of line perpendicular to this line is m₂= 1 3 General equation line passing through point (x₁, y₁ ) is (y-y₁ )=m (x-x₁ ) Here m= 1 3 and (x₁, y₁ )=(2,2) . So, y-2= 1 3 (x-2) y-2= x 3 - 2 3 y= x 3 +2- 2 3 y= x 3 + 4 3 So, y -axis intercept is, 4 3

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