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.

Question

 

 

y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

Answer 1

The line 5x-2y=-6 has slope m=5/2  [note: convert Ax+By=C to y=mx+b once and forever and determine that the slope is (-A/B)].  All perpendicular lines have slope that is the negative reciprocal (that is, -1/m), so their slope is (-2/5) and their equation, in Standard Form, looks like 2x+5y=D and we need a point to determine D.

      2(5)+5(-4)=D

          -10=D

The perpendicular line is:   2x+5y=-10      So, check variations of that formula:

 

         y = –x – 2
⇒      2x + 5y = −10
         2x − 5y = −10
         y + 4 = –(x – 5)
         y – 4 = (x + 5)