Question

A line is perpendicular to y = -4x-2
and intersects the point (0,9).
What is the equation of this
perpendicular line?

Answer 1

Answer:

$y = \dfrac{1}{4}x+9$

Step-by-step explanation:

The product of slope of perpendicular lines are (-1).

Slope intercept form: y = mx +b

Here, m is slope and b is y-intercept.

        y = -4x - 2.

Slope m₁ = -4

$\text{slope of the required line = m = \dfrac{-1}{m_1} }$

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

The line is passing through the point(0 , 9)

Substitute the slope and point in the equation of line in point-slope form:                        

                  $\boxed{y - y_1 = m(x - x_1) }$

               $y - 9 = \dfrac{1}{4}(x - 0)\\\\\\y - 9 = \dfrac{1}{4}x\\\\~~~~~~ y = \dfrac{1}{4}x+9$