What is the slope of a line perpendicular to y = - 7/4x?

A line is perpendiculat to another which has a slope of m if the perpendicular line has a slope of - 1/m.

That means that if the product of slopes of two lines is - 1, the two lines are perpendicular.

Here, y1=-7/4x, or m=-7/4

The perpendicular should have a slope of - 1/m=-1 / (-7/4) = 4/7