Find the equation


Find the equation of the tangent line to the curve $y=x^{2}-2 x+7$ which is

parallel to the line $2 x-y+9=0$


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 $)=2$

$2 x-2=2$


since this point lies on the curve, we can find $y$ by substituting $x$

$y=2^{2}-2 \times 2+7$


therefore, the equation of the tangent is


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