Question

is y = -x - 8 and y = -x + 3 perpendicular

Answer 1

Two lines are perpendicular if and only if their slopes fullfil:

$m_1m_2=-1$

Then we need to find the slopes of each line. We notice that both lines are written in the slope intercerpt form:

$y=mx+b$

Equation y=-x-8.

Comparing this equation with the general one given above we have that:

$m_1=-1$

Equation y=-x+3

Comparing this equation with the general one given above we have that:

$m_2=-1$

Plugging this values in the condition we have that:

$m_1m_2=(-1)(-1)=1$

Since the result is not -1 we conclude that the condition is not fullfil, therefore the lines are not perpendicular between each other.