Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 3, y, equals, 453x−3y=45. Fully simplify your answer.

The equation of the line given is 3x - 3y = 45.

Step 1: We first need to find the slope of the given line. To do this, we can rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.

3x - 3y = 45 can be rewritten as y = x - 15.

So, the slope of the given line is 1.

Step 2: The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

The reciprocal of 1 is 1, and the negative of 1 is -1.

So, the slope of the line perpendicular to the given line is -1.