What is an equation of the line that is perpendicular to y-4=2(x-6) and passes through the point (-3,-5)?

The perpendicular equation is y = -1/2x - 6.5.

You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 2 we flip it and make it a negative and the new slope is -1/2. Now we can use that and the point to get the y intercept using slope intercept form.

y = mx + b

-5 = (-1/2)(-3) + b

-5 = 3/2 + b

-6.5 = b

And now we can use our new slope and new intercept to model the equation.

y = -1/2x - 6.5