Question

Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = −3 and g'(6) = 5. (Enter your answer as an equation in terms of y and x.)

Answer 1

The equation of tangent line is
`y=5x-33`

Explanation:

We need to find out the equation of tangent line.

Given :- g(6)=−3 and g'(6)= 5

If g(6)=−3

then the point on the line for the required tangent is (6,−3)

If g'(6)= 5

then the slope of the tangent at that point is 45

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))=5(x-6)`

`(y+3)=(5x-30)`

subtract both the sides by 3,

`y+3-3=5x-30-3`

`y=5x-33`

Therefore, the equation of tangent line is
`y=5x-33`