Final answer:
The equation of line n that is parallel to line k and passes through the point (2, -4) is y = 2x - 8.
Step-by-step explanation:
To find the equation of a line parallel to line k that passes through the point (2,-4), we can use the fact that parallel lines have the same slope.
Since the equation of line k is y = 2x + 1, the slope of the parallel line will also be 2.
Using the point-slope form of a linear equation,
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope, we can substitute the values to get the equation:
y - (-4) = 2(x - 2)
This can be simplified to y = 2x - 8, which is the equation of line n.