The equation of the line perpendicular to 42 - 2y = 6 and passing through (4, -4) is y + 2x = -12.
To find the equation of a line perpendicular to a given line, you need to know that the slopes of perpendicular lines are negative reciprocals of each other.
The given line can be rewritten in slope-intercept form (y = mx + b) as y = 21 - (1/2)x. The slope of this line is -1/2.
The slope of a line perpendicular to this line will be the negative reciprocal of -1/2, which is 2.
Using the slope-intercept form of a line, the equation of the line perpendicular to the given line and passing through (4, -4) can be found as follows:
y - (-4) = 2(x - 4)
y + 2x = -12