Let's begin by listing out the given information:
Equation of line: y = -2x + 1
Point C (x, y) = (4, 7)
[tex]y=-2x+1\Rightarrow m=-2[/tex]Parallel lines have the same slope. As such, the slope of the parallel line must also be -2
Using point slope equation of a straight line, we have:
[tex]\begin{gathered} y-y_1=-2\left(x-x_1\right) \\ at(x,y)=(4,7) \\ y-7=-2(x-4) \\ y-7=-2x+8 \\ y=-2x+8+7 \\ y=-2x+15 \end{gathered}[/tex]