equation of any straight line is ... y=mx+b ... m=slope, b=y intercept
dy/dx = f'(x) is the slope at any point and is also the slope of the tangent line. Thus m = f'(x). Now if you know the point (x1,y1) and the slope you can find b by substituting the x1,y1 values of the point and calculate b by using b=y1-mx1.
This problem dy/dx=2x ... if x1,y1 is (example) (1,1), then m=2*x1=2*1=2. Also b = y1-mx1 = 1-2*1=-1.
The equation for the tangent line is now ... y=2x-1
