Write the equation for a line that passes through (5,-4) and is perpendicular to the linear function 2x - 10y = 0

y  =  -5x -24

Step-by-step explanation:

 Given parameters:

    Coordinates of the line = (5, - 4)

   Linear function ;

                            2x - 10y = 0

Solution:

The equation of the line perpendicular to this line will have a slope that is the a negative inverse of the given line;

                          2x - 10y = 0

Equation of a line is given as;

                          y  = mx + c

y and x are the coordinates

  m is the slope

  c is the y-intercept

We find the slope and y-intercept of the new line;

                      From:  2x - 10y = 0

 Rewrite;

                        -10y = -2x

                              y  = x

                              y = x

The slope of this line is   , the line perpendicular will have slope of -5

For the new line;

                   y  = mx + c

 let us find c;

                    -4  = -5( -4)  + c

                   -4  = 20 + c

                    c  = -20 - 4

                     c = -24

The equation of the perpendicular line is;

            y  =  -5x -24

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