Find an equation of the line:
through the point (2, −4) with ay-intercept of −2.

The slope-intercept form: y = mx + b

m - the slope
b - y-intercept

y-intercept is -2, therefore y = mx - 2.

The line throught the point (2;-4). Subtitute the coordinates to the equation of the line:

-4 = 2m - 2    |add 2 to both sides

2m = -2    |divide both sides by 2

m = -1

y = -x - 2