If you have a function f(x) and you translate it a units downward, you obtain a new function g(x) given by:
f(x) = g(x) - a
for the present case, you can notice that the original function has a slope of -3 and a y-intercept of 6, then, based on the general expression for an equation of a line, you have:
y = mx + b
m: slope = -3
b: y-intercept = 6
y = -3x + 6
after the translation you get:
y = -3x + 6 - 2
y = -3x + 4
Hence, the equation y = -3x + 4 represents the trasnlated line
