First put the given equations into the form, y = mx + c, as follows:
[tex]y=\frac{4}{7}x+\frac{3}{14}[/tex]
[tex]y=\frac{k}{7}x+\frac{10}{7}[/tex]
For perpendicularity, the product of the slopes must equal negative one.
[tex]\frac{k}{7}\times\frac{4}{7}=-1[/tex]
Solving for k, we get:
[tex]k=-\frac{49}{4}[/tex]
The correct choice is C.
