Question

Are the lines y = –x + 8 and 4x + 4y = 12 perpendicular? Explain.

Yes; their slopes are equal.

No; their slopes are not equal

No; their slopes are not opposite reciprocals.

Yes; their slopes have product –1.

Answer 1

we have that
y = –x + 8
and
4x + 4y = 12

we know that
if two lines are perpendicular
so
m1*m2=-1

step 1
find the slope of the lines
y = –x + 8 -------> m1=-1

4x + 4y = 12-----> x+y=3 (divided by 4 all expression)
y=3-x
m2=-1

therefore
m1=m2
the lines are parallel

the answer is
No; their slopes are not opposite reciprocals.

see the attached figure