General Equation of a perpendicular line

Question

Write the general equation of the line perependicular to x-4y-1=0 and 5 units above the origin.

Answer 1

The equation x - 4y - 1=0

Convert the equation to slope intercept form (y = mx + c).

x - 4y - 1=0

4y = x -1

y = (1/4)x - (1/4)

Here slope is 1/4.

Slope of the perpendicular line to the given line is m = -1/(1/4) = - 4

So perpendicular line equation is y = -4x + b

Here, b is the y - intercept

Substitute b = 5 in above equation.

y = -4x + 5