Question

What equation represents the line that passes through (2,4), and is perpendicular to the graph y = 1/3x-1?Answer choices are y=1/3x+10y=3x+10y= -3x-2y=-3x+10

Answer 1

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:

$y=\frac{1}{3}x-1$

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.

$y-y_1=m(x-x_1)$

Replace it with the point coordinates and the slope:

$\begin{gathered} y-4=-3(x-2) \\ y-4=-3x+6 \\ y=-3x+6+4 \\ y=-3x+10 \end{gathered}$

The equation for the perpendicular line is y=-3x+10 and the correct choice is the last one.