379. Form the equation of the tangent to the parabola $y=x^{2}$ $-4 x$ at the point with abscissa $x_{0}=1$.
Solution. Let's determine the ordinate $y_{0}$ of the point of tangency by substituting the abscissa value $x_{0}=1$ into the equation of the parabola; we have $y_{0}=1-4 \cdot 1=$ $=-3$.

To find the slope of the tangent, we compute the value of the derivative at the point of tangency: $f^{\prime}(x)=2 x-4 ; k=f^{\prime}(1)=-2$.

Now, knowing the point ( $1 ;-3$ ) and the slope $k=y^{\prime}=-2$, we can write the equation of the tangent line:

$$
y+3=-2(x-1), y+3=-2 x+2 \text { or } y=-2 x-1
$$