Question

Which is the equation of a line perpendicular to the line 2x-5y=5
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A. 2x+5y=-3

B. 2x-y=-1

C. 2x-5y=11

D. 10x+4y=3

Answer 1

        Equation of the line perpendicular to the line 2x - 5y = 5 has been given in Option (D)

Property for the perpendicular lines:

•  If the equation of a line is,

          y = m₁x + b

          And another is,

          y = m₂x + c

          Both the lines will be perpendicular if m₁ × m₂ = -1

Given in the question,

• Equation of the line → 2x - 5y = 5

                                          → $y=\frac{1}{5}(2x-5)$

        Slope of this line → m₁ = $\frac{2}{5}$

        If another line perpendicular to the line given is m₂,

        m₁ × m₂ = -1

        $\frac{2}{5}\times m_2=-1$

        $m_2=-\frac{5}{2}$

From the given options,

A). 2x + 5y = -3

     5y = -2x - 3

     $y=-\frac{2}{5}x-\frac{3}{5}$

     Slope of the line = $-\frac{2}{5}$

B). 2x - y = -1

     y = 2x + 1

     Slope of the line = 2

C). 2x - 5y = 11

     5y = 11 - 2x

     $y=-\frac{2}{5}x+\frac{11}{5}$

     Slope of the line = $-\frac{2}{5}$

D). 10x + 4y = 3

     4y = -10x + 3

     $y=-\frac{5}{2}x+\frac{3}{4}$

     Slope of the line = $-\frac{5}{2}$

  Hence, slope of the perpendicular line matches with the slope of the line given in Option D.

         Therefore, Option (D) will be the correct option,

Learn more about the property of the perpendicular lines here,

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