Question 290635
{{{f(x) = 4/x}}}
{{{y = 4/x}}}
{{{y = 4x^(-1)}}}
Find the slope (dy/dx) at x = 5
{{{dy/dx = -4x^(-2)}}} 
{{{dy/dx = -4/x^2}}} and at x = 5,
{{{dy/dx = -4/25}}}, so...
{{{y = (-4/25)x+b}}} Substitute x = 5 and y = 4/5
{{{4/5 = (-4/25)(5)+b}}}
{{{4/5 = (-4/5)+b}}} Solve for b. Add {{{4/5}}} to both sides.
{{{8/5 = b}}} so finally...
{{{highlight(y = (-4/25)x+8/5)}}}