Answer to Question #318598 in Calculus for Joy.

Question

Find an equation of the tangent line to the curve 𝑦 = 2𝑥 2 + 3 that is parallel to the line 8𝑥 – 𝑦 + 3 = 0

Answer 1

$8x-y +3=0 --> y = 8x +3 = mx + b$

A line parallel to y = 8x+3 will have the same slope, m=8. The slope is also the derivative of y=2x²+3

y' = 4x = 8 --> x = 2

y = 2(2)^2+3 = 11. So the intersection point is (2,11)

To get the equation for the line going through that point

y-11 = 8(x-2) --> y = 8x-16+11 = 8x-5