Find equations of the lines that pass through the given point and are parallel to and perpendicular to the given line. \( x-2=0,(7,-1) \) (a) parallel to the given line (b) perpendicular to the given line (

The given line is x - 2 = 0, which can be rewritten as x = 2. This represents a vertical line where the x-coordinate is always 2. (a) Lines parallel to a vertical line are also vertical. Therefore, any line parallel to x = 2 will have the form x = k, where k is a constant. Since the line must pass through the point (7, -1), the x-coordinate of the point, 7, must equal k. Thus, the equation of the line is:   x = 7 (b) Lines perpendicular to a vertical line are horizontal lines. Horizontal lines have equations of the form y = c, where c is a constant. Since the line must pass through (7, -1), the y-coordinate of the point, -1, must equal c. Thus, the equation of the line is:   y = -1