Find the slope of a line perpendicular to the line whose equation is 3x-3y=63 Fully simplify your answer.

To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line.<br /><br />The equation of the given line is $3x-3y=63$. We can rewrite this equation in slope-intercept form, which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />To do this, we can isolate $y$ on one side of the equation:<br /><br />$3x-3y=63$<br />$-3y=-3x+63$<br />$y=x-21$<br /><br />From this equation, we can see that the slope of the given line is $1$.<br /><br />The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Therefore, the slope of the line perpendicular to the given line is $-1$.<br /><br />So, the slope of a line perpendicular to the line whose equation is $3x-3y=63$ is $-1$.