Answer:
To find the slope of the parallel and perpendicular lines to the equation y = 3/4x + 4, we need to use the fact that parallel lines have the same slope, while perpendicular lines have opposite reciprocal slopes.
The given equation is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
Therefore, the slope of the given line y = 3/4x + 4 is 3/4.
To find the slope of a line parallel to this one, we know that it must have the same slope. Therefore, the slope of the parallel line is also 3/4.
To find the slope of a line perpendicular to this one, we need to take the opposite reciprocal of the slope. The opposite reciprocal of 3/4 is -4/3. Therefore, the slope of the perpendicular line is -4/3.
In summary, the slope of the parallel line is 3/4, and the slope of the perpendicular line is -4/3.