Final answer:
To find the equation of a line parallel to line L and passing through a given point, first find the slope of line L. Then, use the point-slope form of a linear equation to write the equation of the parallel line.
Step-by-step explanation:
To find an equation of the line that is parallel to line L and passes through the point (5, -11), we need to determine the slope of line L and then use it to form the equation of the parallel line.
First, we find the slope of line L using the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the given points, we get slope = (4 - 12) / (10 - 0) = -8 / 10 = -0.8.
Now, we can use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the coordinates and slope, we get: y + 11 = -0.8(x - 5).
By simplifying the equation, we have the final equation of the parallel line: y = -0.8x + 15.4.