The equation of line wx is y = −2x − 5. write an equation of a line perpendicular to line wx in slope-intercept form that contains point (−1, −2).

Y = -2x - 5
m = -2

The perpendicular line has a negative reciprocal slope.
m = 1/2

You are also given a point, so use the point slope formula.

y - y1 = m(x - x1)
y + 2 = 1/2(x + 1)
y + 2 = 1/2x + 1/2
y = 1/2x - 3/2

So the line perpendicular to y = -2x - 5 in slope intercept form is:
y = 1/2x - 3/2
or
y = 0.5x - 1.5