Question

Indicate the equation of the given line in standard form. The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6,5).​

Answer 1

Given parameters:

Coordinates of end points =  (2, -3) and (-6,5).​

 Slope of line  = $\frac{9}{7}$

Unknown:

Equation of the line with the given slope = ?

Solution:

Let us find the coordinates of the mid-point of the line given.

   Since the end points are (2, -3) and (-6,5);

   Midpoint;

            x, y = $\frac{x_{1} + x_{2} }{2}$ , $\frac{y_{1} + y_{2} }{2}$  

            x, y = $\frac{2 + (-6)}{2}$  ,  $\frac{-3 + 5}{2}$   = -2 , 1

The coordinate of the mid point = -2,1

Equation of a line is;

                  y = mx + c

x and y are the coordinates

     m is the slope

     c is the y intercept

We need to find c in order to fully develop our equation;

             y = mx + c

              y = 1 , x = -2 and m = $\frac{9}{7}$

So,

           1 = $\frac{9}{7}$ x (-2) + c

            c  = 1 + $\frac{18}{7}$   = $\frac{25}{7}$

Now, the equation of the line is;

              y = -2x + $\frac{25}{7}$  

Multiply through by 7,

            7y = -14x + 25

The equation of the line is 7y = -14x + 25