Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? check all that apply. y = –x – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –(x – 5) y – 4 = (x + 5)

A standard-form equation for the perpendicular line will have the x- and y-coefficients swapped and one of them negated. (This gives a line with a slope that is the negative reciprocal of the original line, as is required for a perpendicular line.) Thus, you can look for an equation of the form
  2x +5y = c
for some constant c that make the line go through the required point. This is matched by the 2nd selection. It also tells you the coefficients of x and y will be in the ratio 2:5. The only other choice that has coefficients like this is the 3rd choice, but it has the sign wrong.

The only appropriate selectin is
  2x + 5y = -10