Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options. y = –Two-fifthsx – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –Two-fifths(x – 5) y – 4 = Five-halves(x + 5)

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:[tex]y = mx + b[/tex]Where:m: It's the slopeb: It is the cut-off point with the y axisOn the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:[tex]m_ {1} * m_ {2} = - 1[/tex]The given line is:[tex]5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3[/tex]So we have:[tex]m_ {1} = \frac {5} {2}[/tex]We find [tex]m_ {2}:[/tex][tex]m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}[/tex]So, a line perpendicular to the one given is of the form:[tex]y = - \frac {2} {5} x + b[/tex]We substitute the given point to find "b":[tex]-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2[/tex]Finally we have:[tex]y = - \frac {2} {5} x-2[/tex]In point-slope form we have:[tex]y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)[/tex]ANswer:[tex]y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)[/tex]