It is given that tangent to the curve y² = 4x

Then differentiating with respect to x, we have,

Then, the equation of the tangent at any given point (x,y) is given by,

The given line is y = x + 1

⇒ Slope of the line = 1

The line y = x + 1 is a tangent to the given curve if the slope of the line is equal to the slope of the tangent.

Also, the line must intersect the curve.

Then, we have,

⇒ y =2

Now, y = x+1

⇒ x = y -1

⇒ x = 2-1 = 1

Therefore, the line y = x+1 is a tangent to the given curve at the point (1, 2).