Calculus of a Single Variable, Chapter 2, 2.1, Section 2.1, Problem 36

The slope of the line 3x-y-4=0 and the lines parallel to it will be same.
3x-y-4=0
y+4=3x
y=3x-4
Therefore the slope(m) of the line is the coefficient of the x = 3
The slope of the tangent line to the graph f(x) is the derivative of the f(x)
f'(x)=3x^2
Since the tangent line to the graph is parallel to the given line
Therefore 3x^2=3
x^2=1
x=1,-1
The y coordinate can be found by substituting the value of x in the function.
for x=1 y=1^3+2=3
for x=-1 y=(-1)^3+2=1
The equation of the tangent line can be written using the point slope form of the equation.
y-y_1=m(x-x_1)
y-3=3(x-1)
y-3=3x-3
y=3x
y-1=3(x-(-1)
y-1=3x+3
y=3x+4