Question

Find the equation of a line passing through 5,5 and 5,-5

Answer 1

Given:

Two points of a co-ordinate system (5,5) and (5,-5)

To Find:

Equation of a Straight line passing through the points (5,5) and (5,-5)

Solution:

1. Consider the given points as P(5,5) and Q(5,-5).
2. According to the properties of straight lines,  

       Let A(x1,y1) B(x2,y2) be any two points in the 2D co-ordinate system,

       Then , The equation of the straight line passing through the points    

       A(x1,y1) and B(x2,y2) is given by : (y-y1) = $\frac{y2-y1}{x2-x1}$(x-x1) where  

       x1,x2,y1,y2 are the co-ordinates in the plane. Here the expression

       $\frac{y2-y1}{x2-x1}$  is the equation of  slope of the straight line which is    

       denoted by m.

    3.Using the above mathematical formula , On substitution we can obtain  

        the equation of the straight line. From the given data the value of

        (x1,y1) (x2,y2) is (5,5) (5,-5) respectively.

    4. On substitution the equation is:

            =>(y-5) = [(-5 + 5)/(-5-5)] (x-5)

            => y-5=0 (Since the Right hand side is Zero after the calculations)

            => y=5.

    Therefore,

                        The Equation of the line passing through the points (5,5)  

    and (5,-5) is y=5.