Question

Find an equation of the tangent line to the graph of `y=g(x)` at `x=5` if `g(5) = -3` and `g'(5) = 4`? Can you explain this to me in detail?

Answer 1

`y = 4x - 23`

Explanation:

This tells us that when `x = 5`, `y = -3`. Also, when the derivative equals `5`, the slope of the tangent is `4`.

This is all we need to find the equation of the tangent.

`y - y_1= m(x- x_1)`

`y- (-3) = 4(x - 5)`

`y+ 3 = 4x - 20`

`y = 4x - 23`

Hopefully this helps!