When does the proportion form of newton's second law take the form of an equation?

Newton's law of motion has three parts. The second of which states that the force needed to move an object is directly proportional to the acceleration of the motion. The proportion can be written as,
              F = ka
where k is the constant of proportionality. This can be substituted with the mass of the object such that the equation would become. 
                F = ma
where F is force, m is mass, and a is acceleration. 

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