Explanation:
To show that two lines are parallel, we need to demonstrate that their slopes are equal.
The equation of line L is given as y=5x+1. This equation is already in slope-intercept form, where the slope is the coefficient of x, which is 5.
Now, let's rewrite the equation of the second line, 2y-10x+3=0, in slope-intercept form:
2y-10x+3=0
2y=10x-3
y=5x-3/2
So the slope of the second line is also 5.
Since both lines have the same slope of 5, we can conclude that they are parallel to each other.