Question

Write an equation for the line that is
perpendicular to the line y = 4x + 9
and goes through the point (2, 8).

Answer 1

Answer:

$\sf y =\dfrac{-1}{4}x+\dfrac{17}{2}$

Step-by-step explanation:

Equation of the line: y =mx + b

        where m is slope and b is y-intercept.

y = 4x + 9

Slope = m₁ = 4

$\sf \text{Slope of the perpendicular line = \dfrac{-1}{m_1} }$

                                                $\sf \boxed{m = \dfrac{-1}{4}}$

  $\sf y =\dfrac{-1}{4}x +b$

The point (2,8) passes through the line. Substitute in the above equation to find 'b'.

     $\sf 8 = \dfrac{-1}{4}*2+b\\\\\\ 8 = \dfrac{-1}{2}+b$

$\sf 8+\dfrac{1}{2}=b\\\\ \dfrac{16}{2}+\dfrac{1}{2}=b\\\\ \boxed{b=\dfrac{17}{2}}$

     Equation of the line:

                    $\sf y =\dfrac{-1}{4}x + \dfrac{17}{2}$