Respuesta :
When you are looking for a line perpendicular to a known line, you have to keep in mind that the slope of the permendicular line will be the inverse negative of the first line.
So for the given line:
[tex]y=\frac{1}{3}x-1[/tex]The slope is m=1/3
The slope for the perpendicular will be the inverse negative:
m=-3
Using this slope and the given point (2, 4), you can apply the point-slope formula to determine de equation of the perpendicular line.
[tex]y-y_1=m(x-x_1)[/tex]Replace it with the point coordinates and the slope:
[tex]\begin{gathered} y-4=-3(x-2) \\ y-4=-3x+6 \\ y=-3x+6+4 \\ y=-3x+10 \end{gathered}[/tex]The equation for the perpendicular line is y=-3x+10 and the correct choice is the last one.
