Line m is represented by the equation y + 2 = 3/2(x + 4). The last one just to make sure of something here.
The slope of the given line = m = 3/2 perpindicular is - 1/m = -2/3
which answer(s) have slope = -2/3 ????
When the equation is in this form ( where the coefficient of y is 1 ),
we can pick off the slope of the line as the coefficient of x .
Here, the coefficient of x is \(\frac32\) so
slope of line m = \(\frac32\)
slope of line perpendicular to m = the negative reciprocal of \(\frac32\)
slope of line perpendicular to m = \(-\frac23\)
The equations that have \(-\frac23\) (or something equaivalent to \(-\frac23\) ) as the coefficient of x represent lines perpendicular to m