Find the equation


Find the equation of the tangent line to the curve $y=x^{2}+4 x-16$ which is parallel to the line $3 x-y+1=0$.


finding the slope of the tangent by differentiating the curve

$\frac{d y}{d x}=2 x+4$

$m($ tangent $)=2 x+4$

equation of tangent is given by $y-y_{1}=m($ tangent $)\left(x-x_{1}\right)$

now comparing the slope of a tangent with the given equation

$2 x+4=3$


Now substituting the value of $x$ in the curve to find $y$


Therefore, the equation of tangent parallel to the given line is


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