The equation of line t is y=
–
3x–9. Perpendicular to line t is line u, which passes through the point (6,
–
3). What is the equation of line u?

To find the equation of line \( u \) that is perpendicular to line \( t \) and passes through the point \( (6, -3) \), we can follow these steps:

1. **Identify the slope of line \( t \)**:
   The equation of line \( t \) is given as \( y = -3x - 9 \). The slope of this line \( t \) is \( m_t = -3 \).

2. **Find the slope of line \( u \)**:
   Since line \( u \) is perpendicular to line \( t \), the slope of line \( u \) (denoted as \( m_u \)) is the negative reciprocal of the slope of line \( t \). 
   \[
   m_u = \frac{1}{3}
   \]

3. **Use the point-slope form of the equation of a line**:
   The point-slope form is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is a point on the line. Here, \( (x_1, y_1) = (6, -3) \) and \( m = \frac{1}{3} \).

4. **Substitute the point and slope into the point-slope form**:
   \[
   y - (-3) = \frac{1}{3}(x - 6)
   \]
   Simplifying this:
   \[
   y + 3 =

Discover how to find the equation of a line perpendicular to y = -3x - 9 that passes through the point (6, -3). This problem involves understanding perpendicular slopes and applying the point-slope form of a line equation. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation