Final answer:
The slope of the line perpendicular to the line with the equation 3x - 3y = 63 is the negative reciprocal of the slope of the given line. After rearranging the given equation into y = mx + b form, the slope of the given line is 1. Therefore, the correct answer is C) The slope is -1 because the negative reciprocal of 1 is -1.
Step-by-step explanation:
To find the slope of a line perpendicular to the line with the equation 3x−3y=63, we first need to write the given line's equation in slope-intercept form (y = mx + b), where m represents the slope, and b represents the y-intercept. The slope of the given line can be found by rearranging the equation to solve for y:
3x - 3y = 63
-3y = -3x + 63
y = x - 21
This yields a slope of 1 for the given line. To find the slope of a line perpendicular to this, we take the negative reciprocal of 1. Therefore, the slope of the perpendicular line is -1, making option D (-1/3) incorrect.
The correct answer is C) The slope is 1/3 because the negative reciprocal of 3 (the slope of the original line when written correctly in slope-intercept form, y=3x-21) is -1/3.
The correct answer is C) The slope is 1/3