The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equation is expressed as
3x - 18y = - 378
We would add 18y to both sides of the equation. We have
3x - 18y + 18y = - 378 + 18y
3x = - 378 + 18y
We would add 378 to both sides of the equation. We have
3x + 378 = - 378 + 378 + 18y
3x + 378 = 18y
18y = 3x + 378
Dividing both sides of the equation by 18, we have
18y/18 = 3x/18 + 378/18
y = x/6 + 21
By comparing this equation with the slope intercept equation,
m = 1/6
Recall, if two lines are parallel, it means that they have the same slope. This means that the slope of a line parallel to the line whose equation is 3x- 18y = - 378 is 1/6