Are the lines y = –x – 4 and 5x + 5y = 20 perpendicular? explain.
a.
yes, their slopes are equal.
b.
yes, their slopes have a product of –1.
c.
no, their slopes are not equal.
d.
no, their slopes are not opposite reciprocals.

Y=mx+b
m=slope

ax+by=c
-a/b=slope

if slopes muliply to -1 then they are perpendicular

given

y=-1x-4
slope is -1

5x+5y=20
slope=-5/5=-1

-1 timesm -1=1≠-1
not perpendicular

D is answer

In second equation, 5x + 5y = 20
5y = -5x + 20
Divide the equation by 5, 
y = -x + 4
Here, Slope = -1

Perpendicular line must have slope equal to 1 [ which is opposite & reciprocal ]
But in y = -x - 4, slope = -1 so they are not perpendicular.

In short, Your Answer would be Option D) No, their slopes are not opposite reciprocals.

Hope this helps!

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