This is the concept of algebra, to get the slope of the line we need to rewrite the equation in slope intercept form y=mx+c, where m=slope, c=y-intercept.
Therefore re-writing our expression in slope-intercept form we get:
7x-3y=10
-3y=-7x+10
y=7/3x-10/3
The slope=7/3
hence we conclude that the slope of the line perpendicular to this is -3/7