Question

How do you find an equation of the tangent line to the graph of `y = g(x)` at x = 5 if `g(5) = −4` and `g'(5) = 3`?

Answer 1

Basically the slope `m` of the tangent line is `g'(5)=3` and the point of tangence is going to be `x=5, y=g(5)=-4`. So, using the relationship:
`y-y_0=m(x-x_0)`
you get:
`y+4=3(x-5)`
`y=3x-19`
which is the equation of the tangent line.

Hope it helps!