Subjects algebra

Perpendicular Line 5442Fc

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Question: Find the equation for the line that passes through the point $(2,2)$, and that is perpendicular to the line with the equation $x = -1$.
1. **State the problem:** We need to find the equation of a line that passes through the point $(2,2)$ and is perpendicular to the line $x = -1$. 2. **Understand the given line:** The line $x = -1$ is a vertical line where all points have $x$-coordinate $-1$. 3. **Perpendicular line rule:** A line perpendicular to a vertical line is a horizontal line. 4. **Equation of a horizontal line:** A horizontal line has the form $y = c$, where $c$ is the constant $y$-coordinate of any point on the line. 5. **Find $c$ using the point $(2,2)$:** Since the line passes through $(2,2)$, the $y$-coordinate is $2$, so the equation is: $$y = 2$$ **Final answer:** The equation of the line perpendicular to $x = -1$ and passing through $(2,2)$ is $$y = 2$$.