Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 3, y, equals, 633x−3y=63. Fully simplify your answer.
To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
To find the slope of the given line, we can rewrite its equation in slope-intercept form (y = mx + b), where m is the slope.
633x - 3y = 63
Rewriting in slope-intercept form,
-3y = -633x + 63
Dividing both sides by -3,
y = 211x - 21
Comparing this equation to y = mx + b, we see that the slope is 211.
The negative reciprocal of 211 is -1/211.
Therefore, the slope of a line perpendicular to the given line is -1/211.