Question

Find an equation of the tangent line to the graph of

Answer 1

Answer:

$y- y_o = m(x-x_o)$

For this case m represent the slope and is given by $m= g'(4) = 2$ and from the other condition given we know that $x_o = 4, y_o =-3$. And replacing we got:

$y -(-3) = 2 (x-4)$

And if we reorganize the terms we have:

$y+3 = 2x -8$

And subtracting 3 in both sides we got:

$y = 2x -11$

Step-by-step explanation:

For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: $g(4) =-3, g'(4)=2$

So we need a function like this one:

$y- y_o = m(x-x_o)$

For this case m represent the slope and is given by $m= g'(4) = 2$ and from the other condition given we know that $x_o = 4, y_o =-3$. And replacing we got:

$y -(-3)=2(x-4)$

And if we reorganize the terms we have:

$y+3 = 2x -8$

And subtracting 3 in both sides we got:

$y = 2x -11$