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

`y = (1)/(4)x+9`

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 =$(-1)/(m_1)$}`

`\sf m = (-1)/(-4)=(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 = (1)/(4)(x - 0)\\\\\\y - 9 = (1)/(4)x\\\\~~~~~~ y = (1)/(4)x+9`