Question

Write the slope-intercept form of the equation of the line that is perpendicular to and passes through Point X. Show all work for full credit.

Answer 1

Answer:

$y =\dfrac{12}{5}x + 22$

Step-by-step explanation:

Slope-intercept form of line:

First find the slope of the line AB. ie, m

Slope of the perpendicular line = -1/m

(2 , 3)  ⇒ x₁ = 2 & y₁ = 3  

(-10, 8)  ⇒ x₂ = -10 & y₂ = 8

$\boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}$

          $= \dfrac{8-3}{-10-2}\\\\=\dfrac{5}{-12}\\\\=\dfrac{-5}{12}$

$\sf slope \ of \ the \ perpendicular \ line \ m_1 = \dfrac{-1}{m}= -1 \ \div \dfrac{-5}{12}$

                                                   $\sf = -1 * \dfrac{12}{-5}=\dfrac{12}{5}$

Equation of the required line: y = mx + b

       $y =\dfrac{12}{5}x+b$

The line passes through (-5 , 10). Substitute in the above equaiton,

         $10 =\dfrac{12}{5}*(-5) + b\\\\ 10 = (-12) + b$

 10 + 12 = b

        b   = 22

Equation of the line:

  $y =\dfrac{12}{5}x + 22$