https://file.aiquickdraw.com/mathbot/file/1725953641430utybvis3.jpg

To answer the questions about lines \( k \) and \( j \), let's analyze the diagram provided:

1. **Line \( k \)**:
   - It passes through the point \( (-2, 6) \) and intersects the \( y \)-axis at \( (0, 4) \). 
   - With these two points, we can calculate the slope of line \( k \).
   - The slope formula is:
     \[
     m_k = \frac{y_2 - y_1}{x_2 - x_1}
     \]
     Using \( (x_1, y_1) = (-2, 6) \) and \( (x_2, y_2) = (0, 4) \):
     \[
     m_k = \frac{4 - 6}{0 - (-2)} = \frac{-2}{2} = -1
     \]
   - The slope of line \( k \) is \( -1 \), and the \( y \)-intercept is \( 4 \), so the equation of line \( k \) is:
     \[
     y = -x + 4
     \]

2. **Line \( j \)**:
   - Line \( j \) passes through \( (-3, -1) \) and is parallel to line \( k \) (since the arrows suggest they have the same slope).
   - Since parallel lines have the same slope, the slope of line \( j \) is also \( -1 \).
   - To find the equation of line \( j \), we use the point-slope form:
     \[
     y - y_1 = m(x - x_1)
     \]
     Using \( (x_1, y_1) = (-3, -1) \) and \( m = -1 \):
     \[
     y + 1 = -1(x + 3)
     \]
     Simplifying:
     \[
     y + 1 = -x - 3
     \]
     \[
     y = -x - 4
     \]
   - Therefore, the equation of line \( j \) is:
     \[
     y = -x - 4
     \]

### Final answers:
- The equation of line \( k \) is: \( y = -x + 4 \)
- The equation of line \( j \) is: \( y = -x - 4 \)

Let me know if you'd like more details or have further questions!

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Here are 5 related questions:
1. How do we determine the slope of a line given two points?
2. What is the general form of a linear equation?
3. How can you find the equation of a line perpendicular to a given line?
4. How do parallel lines differ in terms of their slopes?
5. What are the steps to converting a point-slope form equation to slope-intercept form?

**Tip**: Always verify the slope and the intercept separately when solving for the equation of a line.

Lines k and n intersect on the y-axis. a. What is the equation of line k? b. What is the equation of line j?

This problem focuses on finding the equations of lines k and j. Learn how to use the slope formula and point-slope form to determine the equations of lines based on their intersections and parallel slopes. Suitable for students in Grades 9-11.

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