Final answer:
The slope of line K, which is parallel to the line y = 4x - 7, is 4 because parallel lines have the same slope.
Step-by-step explanation:
The question asks for the slope of line K which is parallel to the line represented by the equation y = 4x - 7 in the xy-plane. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since line K is parallel to the given line, it must have the same slope. The slope of the given line is 4, as it is the coefficient of x in the equation. Therefore, the slope of line K is also 4.