Final answer:
The equation of the line that is perpendicular to 6x - 12y = 16 and passes through the point (12, -7) is y = -2x + 17.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, first we need to determine the slope of the given line. The equation of the given line is 6x - 12y = 16. We can rewrite this in slope-intercept form (y = mx + b), giving us y = (1/2)x - (4/3). The slope of this line is 1/2. A line that is perpendicular to this will have a slope that is the negative reciprocal, so the slope of the perpendicular line is -2.
Using the point (12, -7) that the perpendicular line passes through, we can use the point-slope form of a line equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Substituting into the formula, we get: y + 7 = -2(x - 12).
Simplifying, we get the equation of the line in slope-intercept form: y = -2x + 17. This is the equation of the line that is perpendicular to the given line and passes through the point (12, -7).