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
y = - 6x/7 + 1
This means that the slope of the given line - 6/7
Recall, if two lines are parallel, it means that they have the same slope. This means that the slope of the line passing through (0, 0) and parallel to the given line is m = - 6/7
We would find the y intercept, x of this parallel line by substituting m = - 6/7, x = 0 and y = 0 into the slope intercept equation. We have
0 = - 6/7 * 0 + c
0 = 0 + c
c = 0
We would substitute m = - 6/7 and c = 0 into the slope intercept equation, the equation of the line is
y = - 6x/7