We need to find the line using the given points.
First, we need to find the slope:
The slope equation is given by:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_1-x_2} \\ \text{Replace using P1(-4,13) and P2(0,-3):} \\ m=\frac{-3-(13)}{0-(-4)}=\frac{-16}{4}=-4 \end{gathered}[/tex]
The slope is equal to 4.
Now, to find the line equation, we need to use the next equation:
[tex]\begin{gathered} y_{}-y_1=m(x_{}-x_1) \\ \text{Replace using P1(-4,13) and m=-}4 \\ y-13=-4(x-(-4)) \\ y-13=-4(x+4) \\ y-13=-4x-16 \\ y=-4x-16+13 \\ \text{Hence, the line is:} \\ y=-4x-3 \end{gathered}[/tex]
Therefore, the correct answer is the fifth option.
