Question 1131074
The y-intercept and the slope are not dependent.  The y-intercept is where x=0, and it is possible in such a plot that the positive values of x are useful but the zero value is not.

one line from the first two points is y-y1=m(x-x1) m slope, (x1, y1) a point
y-4=3(x-7)
y=3x-3
{{{graph(300,300,-10,10,-10,10,3x-3)}}}
Here, when x=1, y=0, but there are no points given where this was an issue.

Also, since the slope between adjacent points is not always 3 , and the slope between the first and last is 15/7, there are different possible lines, and the best slope (minimum least square differences) is regression.  To answer your question, however, positive slopes and negative intercepts are certainly allowable.