Final answer:
The equation for a line that is perpendicular to a given line and passes through a specific point (-9, -2) is 3x - 2y = 10. The option B is correct.
Step-by-step explanation:
In order to formulate the equation for a line perpendicular to a given line and passing through a specified point, the principle that perpendicular lines exhibit slopes as negative reciprocals is applied.
Initially, determine the slope of the given line by converting its equation to the slope-intercept form (y = mx + b), where 'm' denotes the slope.
Subsequently, ascertain the negative reciprocal of this slope to identify the slope of the perpendicular line.
Finally, employ the point-slope form of a linear equation (y - y1 = m(x - x1)), substituting the slope and the coordinates of the point (-9, -2), to establish the equation for the perpendicular line.
Hence, the option B) 3x - 2y = 10 aligns with the calculated parameters, signifying the equation for the line perpendicular to the given line and passing through the designated point.