1Cademy - Finding the Equation of a Line Perpendicular to $$x = 4$$ Through $$(4, -5)$$

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Finding the Equation of a Line Perpendicular to $x = 4$ Through $(4, -5)$

To determine the equation of a line that is perpendicular to the line $x = 4$ and passes through the point $(4, -5)$ , identify the orientation of the original equation. The equation $x = 4$ defines a vertical line. Because perpendicular lines intersect at a right angle, a line perpendicular to a vertical line is inherently horizontal, characterized by the form $y = b$ . Since the required line is constrained to pass through the specific coordinate $(4, -5)$ , every point on this line shares the constant $y$ -coordinate of $-5$ . Consequently, the fully resolved equation for this horizontal perpendicular line is $y = -5$ .