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Mathematics

The slope of a line perpendicular to the line 3x = 4y + 11 is

  1. 34\dfrac{3}{4}

  2. −34-\dfrac{3}{4}

  3. 43\dfrac{4}{3}

  4. −43-\dfrac{4}{3}

Straight Line Eq

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Answer

Given, 3x = 4y + 11.

⇒ 4y = 3x - 11

⇒ y = 34x−114\dfrac{3}{4}x - \dfrac{11}{4}.

Comparing with y = mx + c we get,

Slope (m1) = 34\dfrac{3}{4}.

Let the slope of perpendicular line be m2. Since, lines are perpendicular so,

⇒m1×m2=−1⇒34×m2=−1⇒m2=−43.\Rightarrow m1 \times m2 = -1 \\[1em] \Rightarrow \dfrac{3}{4} \times m2 = -1 \\[1em] \Rightarrow m2 = -\dfrac{4}{3}.

Hence, Option 4 is the correct option.

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