The line defined by the equation 2y+3=-2/3 (x-3) is tangent to the graph of g (x) at x=-3. What is the value of the limit as x approaches - 3 (g (x) - g (-3)) / (x+3)

2y+3=-2/3 (x-3)

minus 3 both sides

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

divide both sides by 2

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

ok, so one thing we can do is evaluate numbers super close to it

when x=3.00001, then the result is aprox - 1.5

when x=2.99999, the result is - 1.5

the value of the limit is - 1.5 or - 3/2