Find the equation of the tangent line to the curve y = x2 – 2x + 7 w

1.	Find the equation of the tangent line to the curve y = x2 – 2x + 7 which is parallel to the line 2x – y + 9 = 0
Answer» finding the slope of the tangent by differentiating the curve \(\frac{dy}{dx}=2x-2\) m(tangent) = 2x – 2 equation of tangent is given by y – y₁ = m(tangent)(x – x₁) now comparing the slope of a tangent with the given equation m(tangent) = 2 2x – 2 = 2 x = 2 since this point lies on the curve, we can find y by substituting x y = 2² – 2 × 2 + 7 y = 7 therefore, the equation of the tangent is y – 7 = 2(x – 2)

Find the equation of the tangent line to the curve y = x2 – 2x + 7 which is parallel to the line 2x – y + 9 = 0

Answer»

finding the slope of the tangent by differentiating the curve

\(\frac{dy}{dx}=2x-2\)

m(tangent) = 2x – 2

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

now comparing the slope of a tangent with the given equation

m(tangent) = 2

2x – 2 = 2

x = 2

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

y = 2² – 2 × 2 + 7

y = 7

therefore, the equation of the tangent is

y – 7 = 2(x – 2)