Question 637444
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,

f(x) = 1/(3x-2)     {{{f(0) = -1/2}}}
f '(x) = {{{(3x-2)*0 - 1*3/(3x-2)^2}}}    ||Quotient Rule
f '(0) = -3/4 = m, the slope of the tangent line at x = 0
y = mx + b
y = (-3/4)x + b    |\using Pt(0,-1/2) to find b
-1/2 = b
y = (-3/4)x -1/2  the EQ of the tangent line  
{{{drawing(300,300,   -6, 6, -6, 6,   grid(1),
circle(0, -.5,0.3),
graph( 300, 300, -6, 6, -6, 6,0, (-3/4)x -1/2 , 1/(3x-2)    ))}}}