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

Question

Philoid · Accepted Answer

finding the slope of the tangent by differentiating the curve

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)