What is the equation of the line through point (2, 1) and perpendicular to the line

D) y= 7/3 X -11/3

Step-by-step explanation:

Using the point slope equation of a line expressed as

y-y0 =m(x-x0)

(x0,y0) is the point on the line

m is the slope

First let us get the slope of the line passing through (-4, 1) and (3, -2)

m = y2-y1/x2-x1

m = -2-1/3+4

m= -3/7

Since yh required line is peependicular to this line, then its slope will be;

M= -1/m

M = -1/(-3/7)

M = 7/3

Get the equation needed

Substitute m = 7/3 an the point (2,1) into the equation above

y - 1= 7/3(x-2)

y = 7x/3-14/3 +1

y= 7x/3 -11/3

Hence option D is correct