Find the tangent to a function

Question

Find the tangent to this

$\displaystyle y={1 \over x+3}$

it's crossing the point $(-2,1)$

I have drawn the lines but I can't calculate it

Answer 1

If you are expected to solve this graphically, you can extend your lines to the x and y axes and calculate the gradient from the two axis intercepts. The intercepts should be integers, so your graphs can be quite precise in this problem :)

If you draw the graphs of $y=\dfrac{1}{x+3}$ and drew a tangent line at the point $(−2,1)$, you would see that the tangent crosses the y-intercept at -1 and the x-intercept at -1. From this, you get the gradient of this tangent as -1 and the equation of the tangent becomes $y=−x−1$.

EDIT: Added stuff from my comment below, though it now gives the answer away...

Answer 2

Hint: The slope of the tangent line at the point $(-2, 1)$ is equal to $\dfrac{dy}{dx}(-2)$.