Originally Posted by

**earboth** Hello,

1. I assume that there is a typo and your function reads:

$\displaystyle y = x^2-7x+5$

2. do you want to find the equation of the tangent line at the graph of your function with the tangent point (1, -1)? If so:

The slope of the tangent has the same value as the gradient of the function in the tangent point.

Calculate the 1st derivation:

$\displaystyle y'=2x+7$ . Now plug in x = 1. You'll get

$\displaystyle y'= 9$ That means the tangent has a slope of m = 9.

Now use point-slope-formula of a straight line:

$\displaystyle (y-(-1))=9(x-1)~\iff~\boxed{y=9x-10}$