I don't get the explanation.
Given that line k passes through point A(4,-5,3) and has direction vector (-2,3,0), the equation of line k can be expressed as:
If only the denominator is 0, then equation 1 is meaningless. (What does that mean)
If when the denominator is 0, we assume that the numerator is also 0 (why?) and the fraction can be any value (why?), then equation 1 can be expressed as:
z=3 (how do you get that?)
Equations 1 and 2 mean the same thing. Equation 2 is usually used.