Question:
Find the equation of the tangent line to the curve $y=x^{2}-2 x+7$ which is
parallel to the line $2 x-y+9=0$
Solution:
finding the slope of the tangent by differentiating the curve
$\frac{d y}{d x}=2 x-2$
$m($ tangent $)=2 x-2$
equation of tangent is given by $y-y_{1}=m(\operatorname{tangent})\left(x-x_{1}\right)$
now comparing the slope of a tangent with the given equation
$\mathrm{m}($ tangent $)=2$
$2 x-2=2$
$x=2$
since this point lies on the curve, we can find $y$ by substituting $x$
$y=2^{2}-2 \times 2+7$
$y=7$
therefore, the equation of the tangent is
$y-7=2(x-2)$