One point of the line is given to be (5, -1) and second point is the y-intercept of the line x - 3y = 6
We can write this equation as:
[tex]x-6=3y \\ \\
y= \frac{1}{3}x-2 [/tex]
So, the y-intercept of the line is -2.
Now we have two points for the new line (5, -1) and (0, -2). Using these we can find the slope
[tex]Slope=m= \frac{-2+1}{0-5}= \frac{1}{5} [/tex]
Using the slope and the point (0, -2) we can write the equation in slope intercept form as:
[tex]y= \frac{1}{5}x-2 [/tex]
Thus the answer to this question is option C. Slope for the new line is 1/5 and the y-intercept is -2
