We have a line, y = -4x + 3, which is the image of a line k after the translation (x, y) --> (x+3, y-4).
We can apply this transformation to a line y = mx +b and then compare it to y = -4x + 3.
Wethen apply the transformation as:

We can now equal the slope and the y-intercept as:

The slope of k is m = -4 and the y-intercept can be calculated as:

Then, as m = -4 and b = 11, we can write line k as y = -4x + 11.