Depending on statements of the problem and requirements imposed in it can be required to address an initial or parametrical way of a task of a straight line. Solving geometrical problems, try to write out all possible options of the equations in advance.
Instruction
1. Check presence of all necessary parameters for drawing up the parametrical equation. Respectively, you will need coordinates of a point, the belonging this straight line and also the directing vector. Any vector passing parallel to this straight line will be that. The Parametrichsky task of a straight line represents a system from two equations x = x0+txt, y = y0+tyt where (h0, u0) - coordinates of the point lying on this straight line, and (tx, ty) - coordinates of the directing vector on axes of abscissa and ordinates, respectively.
2. Do not forget that the parametrical equation assumes need to express existing between two (in case of a straight line) variables by means of of some third parameter.
3. Write down the initial equation of a straight line, proceeding from the data which are available for you: coordinates of the directing vector on the corresponding axes are multipliers of a parametrical variable, and coordinate of the belonging direct dot – free members of the parametrical equation.
4. Pay attention to all conditions registered in a task if it seems to you that there are not enough data. So, the indication of the vectors perpendicular to directing or located to it under a certain corner can become the hint for drawing up the parametrical equation of a straight line. Use conditions of perpendicularity of vectors: it is possible only in case their scalar product is equal to zero.
5. Work out the parametrical equation of the straight line passing through two points: their coordinates give you necessary data for determination of coordinates of the directing vector. Write down two fractions: in numerator of the first there has to be a difference x and coordinates on abscissa axis of one of the points belonging to a straight line in a denominator – the difference between coordinates on abscissa axis of both these points. Write down in the same way fraction for values on ordinate axis. Equate the received fractions to the parameter (it can be designated by letter t) and express through it at first x, then at. The system of the equations which became a result of these transformations will also be the parametrical equation of a straight line.