in the diagram, J is the point (8,7) and K is the point (2,3). Given that JL is parallel to the y-axis and the equation of the line KL is 3y+2x=13

To find the coordinates of point \( L \), we need to use the given information: point \( J \) at \((8, 7)\), point \( K \) at \((2, 3)\), and the equation of the line \( KL \) given by \( 3y + 2x = 13 \).

Since \( JL \) is parallel to the y-axis, the x-coordinate of \( L \) is the same as the x-coordinate of \( J \). Therefore, the x-coordinate of \( L \) is 8. Let's denote \( L \) as \( (8, y_L) \).

Now, we need to find the y-coordinate of \( L \). Since point \( L \) lies on the line \( KL \), we substitute \( x = 8 \) into the equation of the line \( KL \):

\[ 3y + 2(8) = 13 \]
\[ 3y + 16 = 13 \]
\[ 3y = 13 - 16 \]
\[ 3y = -3 \]
\[ y = -1 \]

So, the coordinates of point \( L \) are \((8, -1)\).

Let's summarize:

- Point \( J \) is \((8, 7)\)
- Point \( K \) is \((2, 3)\)
- Point \( L \) is \((8, -1)\)

If you have any questions or need further details, please let me know.

### Additional Questions:
1. How do you find the distance between two points on a coordinate plane?
2. What is the formula for finding the slope of a line given two points?
3. How can you determine if two lines are parallel?
4. What is the y-intercept of the line \( KL \)?
5. How can you find the midpoint of a line segment between two points?
6. What does it mean for a line to be parallel to the y-axis?
7. How do you convert the equation of a line from standard form to slope-intercept form?
8. How do you verify if a point lies on a given line?

### Tip:
When dealing with lines parallel to the axes, remember that parallel to the y-axis means all points on the line have the same x-coordinate, and parallel to the x-axis means all points have the same y-coordinate.

Learn how to find the coordinates of point L on line KL with points J(8, 7) and K(2, 3) given. Detailed step-by-step solution involving coordinate geometry and equations of lines.

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