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To solve this problem, we'll follow these steps:

1. **Identify the slope of line \( s \)**:  
   The equation of line \( s \) is given as \( y = -\frac{1}{3}x - 5 \).  
   The slope of this line is \( m_s = -\frac{1}{3} \).

2. **Determine the slope of line \( t \)**:  
   Since line \( t \) is perpendicular to line \( s \), the slope of line \( t \) is the negative reciprocal of \( m_s \).  
   Therefore, the slope of line \( t \) is \( m_t = 3 \).

3. **Find the equation of line \( t \)**:  
   Line \( t \) passes through the point \( (-2, 9) \), and we know its slope \( m_t = 3 \).  
   We can use the point-slope form of a line equation:  
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting the given point and slope:
   \[
   y - 9 = 3(x + 2)
   \]
   Simplify to get the equation in slope-intercept form \( y = mx + b \):
   \[
   y - 9 = 3x + 6
   \]
   \[
   y = 3x + 15
   \]

Thus, the equation of line \( t \) is \( y = 3x + 15 \).

If you have any questions or would like more details, feel free to ask! 

Here are some related questions:

1. How do you find the slope of a line given two points on the line?
2. What is the relationship between the slopes of two perpendicular lines?
3. How do you convert an equation from standard form to slope-intercept form?
4. How can you verify that two lines are perpendicular using their slopes?
5. What is the general formula for the equation of a line in point-slope form?

**Tip:** Remember, for perpendicular lines, their slopes are negative reciprocals of each other (i.e., \( m_1 \times m_2 = -1 \)).

Line s has an equation of y = -1/3x - 5. Line t is perpendicular to line s and passes through (-2, 9). What is the equation of line t?

Learn how to find the equation of a line perpendicular to another and passing through a specific point. This problem involves concepts of linear equations and slope relationships, suitable for students in Grades 8-10.

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