For two lines to be parallel, they have must the same slope. The slope of the given line is -1/4, hence the slope of the other line must be -1/4 as well.
To determine the equation of the line having the slope of -1/4 and passing through the point (2, -1), we can use the formula below:
[tex]y-y_1=m(x-x_1)[/tex]
Let's plug in the given information above to the formula.
[tex]y-(-1)=-\frac{1}{4}(x-2)[/tex]
Then, solve for y.
[tex]\begin{gathered} y+1=-\frac{1}{4}x+\frac{1}{2} \\ y=-\frac{1}{4}x+\frac{1}{2}-1 \\ y=-\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]
Therefore, the equation of the line must be y = -1/4x - 1/2 (Option C).
