To determine the equation of the line parallel to another line passing through a given point, we need to use the slope of the given line.
Given Points:
Point A: (6, -13)
Point B: (7, 4)
Point C: (-3, 9)
First, let's calculate the slope of the line passing through points B and C using the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1)
m = (4 - 9) / (7 - (-3))
= (-5) / (7 + 3)
= -5/10
= -1/2
Since the line L is parallel to the line passing through points B and C, it will have the same slope (-1/2).
Now, we can use the point-slope form of a linear equation to find the equation of line L:
y - y1 = m(x - x1)
Using point A (6, -13) and the slope (-1/2):
y - (-13) = (-1/2)(x - 6)
y + 13 = (-1/2)x + 3
y = (-1/2)x - 10
Therefore, the equation of the line L passing through point (6, -13) and parallel to the line passing through (7, 4) and (-3, 9) is y = (-1/2)x - 10.