Answer:
The correct answer is D: 6y = 42 - 2x
Step-by-step explanation:
By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other.
If we transform 6y = 42 - 2x into its slope-intercept form, y = mx + b:
6y = 42 - 2x
6y = -2x + 42
Divide both sides by 6 to isolate y:
[tex]\frac{6y}{6} = \frac{-2x + 42}{6}[/tex]
y = [tex]-\frac{1}{3}x + 7[/tex]
Its slope, - 1/3 is the reciprocal of the given question's slope, 3.
Therefore, the correct answer is D, 6y = 42 - 2x
