F Fod the equation of the perper \( (5,3) \) to the line \( 22-y+4=0 \)

It appears you're asking to find the equation of the perpendicular line from the point \( (5, 3) \) to the line represented by the equation \( 22 - y + 4 = 0 \). Let's clarify and solve the problem step-by-step. ### 1. Simplify the Given Line Equation The given line equation is: \[ 22 - y + 4 = 0 \] Combine like terms: \[ 26 - y = 0 \quad \Rightarrow \quad y = 26 \] So, the line is a **horizontal line** at \( y = 26 \). ### 2. Determine the Perpendicular Line Since the given line \( y = 26 \) is horizontal, any line perpendicular to it must be **vertical**. Vertical lines have equations of the form: \[ x = \text{constant} \] ### 3. Find the Specific Perpendicular Line Passing Through \( (5, 3) \) The vertical line must pass through the point \( (5, 3) \). Therefore, the equation of the perpendicular line is: \[ x = 5 \] ### 4. Verification - **Given Line:** \( y = 26 \) (horizontal) - **Perpendicular Line:** \( x = 5 \) (vertical) These two lines are indeed perpendicular, as one is horizontal and the other is vertical. ### Final Answer The equation of the perpendicular line is: \[ \boxed{x = 5} \]