Line x is perpendicular to line y is perpendicular to line z. If the slope of line is 4. What is the slope of line z

See below.

Step-by-step explanation:

Assuming "Line x is perpendicular to line y is perpendicular to line z." means:

x is perpendicular to y y is perpendicular to z

If the slope of one line is 4 then the perpendicular line has a slope - 1/4. Perpendicular lines have negative reciprocal slopes which multiply to - 1.

So 4 * - 1/4 = - 1.

If the slope of x is 4 then the slope of y is - 1/4.

If the slope of y is - 1/4 then the slope of z is 4.