The equation of the line passing through (7, -4) and perpendicular to y = -7x + 12 can be found by first determining the slope of the given line, which is -7. The slope of a line perpendicular to this would be the negative reciprocal of -7, which is 1/7.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point (7, -4) and m is the slope 1/7, we can substitute these values to find the equation of the line.
After simplifying the equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.