Answer:
D.
Step-by-step explanation:
The given line is
[tex]y=-\frac{4}{3}x-4[/tex]
Now, if the new line is parallel to the given one, that means it must have the same slope.
[tex]m=-\frac{4}{3}[/tex]
We also know that the new line passes through point (3,-1).
Then, we use the point-slope formula to find the equation of the new line:
[tex]y-y_{1} =m(x-x_{1} )\\y-(-1)=-\frac{4}{3}(x-3)\\ y=-\frac{4}{3}x+4-1\\ y=-\frac{4}{3}x+3[/tex]
Therefore, the line that passes through (3,-1) and it's parallel to the given line is: [tex]y=-\frac{4}{3}x+3[/tex].
The image attached show these parallel lines.
