Write an equation of the line that passes through (-4,-1) and is perpendicular to the line y=4/3x+6

Perpendicular slope is the opposite reciprocal of the slope given, so perpendicular to 4/3 is - 3/4.

To find the equation that goes through (-4,-1) you can use the formula:

y-y1=m (x-x1) where m is the slope

So plug in the values for y1, x1, and m

y - (-1) = - 3/4 (x - (-4))

y+1 = - 3/4x - 3

Then set the equation in y=mx+b form simply by alienating y, so subtract 1 from both sides and you're done.

y = - 3/4x - 4