Question

How do you 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?

Answer 1

If `g(5) = -3`
then the point on the line for the required tangent is `(5,-3)`

If `g'(5) = 4` then the slope of the tangent at that point is `4`

The tangent line can be specified by the slope-point form of the equation:
`(y-y_1)=m(x-x_1)`
which in this case is
`(y-(-3)) = 4(x-5)`

`y+3 = 4x -20`

`y = 4x -23`