The perpendicular equation is y = -1/3x + 10.
You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 3 we flip it and make it a negative and the new slope is -1/3. Now we can use that and the point to get the y intercept using slope intercept form.
y = mx + b
8 = (-1/3)(6) + b
8 = -2 + b
10 = b
And now we can use our new slope and new intercept to model the equation.
y = -1/3x + 10
