what is the slope intercept form for the line perpendicular to y=2/3x-4 passing through (-5,-6)

The slope-intercept form of a line is:  y = mx + b, where m represents the slope and b represents the y-intercept.

For the line   y = 2/3x - 4,  the slope is  2/3.

Any line perpendicular to that line has a slope that is the negative reciprocal of that slope.

The negative reciprocal of  2/3  is  -3/2.

To find the new equation, start with  y = mx + b.

Its slope is  -3/2  and because it passes through the point  (-5, 6) one of its x-values is  -5  and one of its y-values is  6.  Place these values into  y = mx + b:

                                                      6  =  (-3/2)(-5) + b  

Now, solve for b:                             6  =  15/2  +  b  --->   6  =  7.5 + b  -->  b  = -1.5

Place  m = -3/2  and  b = -1.5  into the slope-intercept form to get:  y  =  -3/2x + -1.5

Simplifying:  y  =  -1.5x - 1.5