If two points are shown, then you can find the equation of the line by connecting the points to find slope and y-intercept.
If only the slope is known, then you can't know the equation since you don't know the y-intercept or any point.
A point on the line helps, but just any other random point on the coordinate plane does not.
With a point on the line and the slope, you can find the equation.
And with 3 points on the coordinate plane you cannot, unless they are all on the line.
So the answers you already have are correct and none of the others are.