Final answer:
To find equations of parallel and perpendicular lines, one uses the original line's slope and the negative reciprocal, respectively. However, without the equation's specifics, we cannot provide particular equations for the lines through the point (7, -4).
Step-by-step explanation:
To find the equation of a line that is parallel to another line, you need to use the same slope. Since a part of the question appears to be missing and we do not have the equation of the original line, I'll use a hypothetical slope value (m).
Assuming our line has the equation y = mx + b, we require a line with the same slope that passes through the point (7, -4). That is, y = mx + c where c can be determined by substituting the point's coordinates into the equation and solving for c.
On the other hand, to find the equation of a line that is perpendicular, we need to use the negative reciprocal of the slope of the original line. If our original line had a slope of m, the perpendicular line will have a slope of -1/m. Once again, we will use the same method of substituting the point's coordinates to find the new y-intercept.
Without the complete equation of the initial line, I am unable to provide a specific answer for the parallel and perpendicular lines passing through (7, -4).