Question

Find an equation of the tangent line L to the curve y = x^2+2, parallel to the line y = 1+3 x. (Hint: What must be the slope of this tangent line?) Graph on the same screen y = x^2+2, y = 1+3 x, and the tangent line L.

Answer 1

if we differentiate y=x^2+2 therefore we get 2x so then we say that line l is parallel to line y=1+3x then 2x=3 therefore x=1.5 so the tangent' gradient = 1.5 we dont have a point on the line so how do we find the full equation this is quite misleading !

Answer 2

this is the hint that was given: (Hint: What must be the slope of this tangent line?)

Answer 3

the slope is 1.5