Answer:
Slope = -4
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, which means that multiplying their slopes result in a product of -1. Given the equation, x - 4y = - 12:
Transform the equation into its slope-intercept form, y = mx + b:
x - 4y = - 12
x - x - 4y = - x - 12
-4y = -x - 12
Divide both sides by -4:
[tex]\frac{-4y}{-4} = \frac{-x - 12}{-4}[/tex]
y = ¼x + 3 ⇒ (This is the slope-intercept form of the given standard equation, x - 4y = - 12).
Since the slope of the given equation is ¼, then it means that its negative reciprocal must be - 4:
(¼) (-4) = -1
Therefore, the slope of the line perpendicular to x - 4y = - 12 is - 4.
