Final answer:
The correct equation for a line perpendicular to y = ⅓x - 1 is A. y = -⅓x + 6, as the slope -⅓ is the negative reciprocal of ⅓.
Step-by-step explanation:
The question provided is asking for an equation of a line that is perpendicular to the given line y = ⅓x - 1. When two lines are perpendicular, their slopes are negative reciprocals of one another. The slope of the given line is ⅓. Therefore, the slope of the line perpendicular to it should be the negative reciprocal, which is ⅓ turned upside down and made negative, resulting in -⅔. To find the equation of a perpendicular line, we should look for an equation among the options where the coefficient of x is -⅔.
The correct answer is A. y = -⅓x + 6 because the slope here is -⅓, which is the negative reciprocal of ⅓. Choices B, C, and D do not have a slope of -⅓; therefore, they are not perpendicular to the original line.