Answer
$(y-1)=2(x-1)$
Work Step by Step
Function: $f(x)=x^2$ Line: $2x-y+1=0$
1. Find the slope $m$ of the given line by putting it into point-slope form:
$y=2x+1$, $m=2$
2. Take the derivative of the function:
$f'(x)=2x$
3. Set $f'(x)$ equal to $m$ and solve for the $x$-coordinate:
$2x=2$
$x=1$
4. Plug in $x$ from part 3 into $f(x)$ to get the $y$-coordinate:
$y=f(1)=(1)^2=1$
Point: $(1,1)$
5. Plug the slope $m$ and the point into the point-slope formula $(y-y_{1})=m(x-x_{1)}$:
$(y-1)=2(x-1)$*
*In most cases point-slope form is sufficient. If not, simply convert into whatever form your professor deems acceptable.
