slope of given line is 3
finding the slope of the tangent by differentiating the curve
\(\frac{dy}{dx}=2x-2\)
m(tangent) = 2x – 2
since both lines are perpendicular to each other
(2x – 2) × 3 = – 1
\(x=\frac{5}{6}\)
since this point lies on the curve, we can find y by substituting x
\(y=\frac{25}{36}-\frac{10}{6}+7=\frac{217}{36}\)
therefore, the equation of the tangent is
\(y-\frac{217}{36}=-\frac{1}{3}(x-\frac{5}{6})\)
