Write an equation of the line passing through point P(4,-6)$that is perpendicular to the line y=-3.

x=


The line given is $ y = -3 $, which is a horizontal line. A line perpendicular to a horizontal line must be a vertical line.

A vertical line has the form $ x = c $, where $ c $ is a constant. Since the line must pass through the point $ P(4, -6) $, the equation of the line will be:

\[
x = 4
\]

This is the equation of the line perpendicular to $ y = -3 $ that passes through the point $ P(4, -6) $.

Would you like further details or have any questions? Here are some related questions to explore:

1. What is the equation of a line parallel to $ y = -3 $ passing through $ P(4, -6) $?
2. How can you find the slope of a line perpendicular to a given horizontal or vertical line?
3. What would be the equation of a line perpendicular to $ y = -3 $ if it passed through a different point, say $ P(2, 5) $?
4. How do the equations of horizontal and vertical lines differ?
5. How can you determine if two lines are perpendicular by using their slopes?

**Tip:** A vertical line always has the form $ x = c $, while a horizontal line has the form $ y = c $.

Write an equation of the line passing through point P(4,-6) that is perpendicular to the line y = -3. x = ?

Learn how to find the equation of a line perpendicular to the horizontal line y = -3 that passes through the point P(4, -6). This problem involves key concepts in coordinate geometry, focusing on the relationship between perpendicular lines. Suitable for students in Grades 7-10.

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