Tell whether the lines through the given points are parallel, perpendicular, or neither. Line 1: (−3, 1), (−7,−2) Line 2: (2,−1), (8, 4)

Neither

Step-by-step explanation:

First we need to find the slope of the line between line 1.

We use the formula:

y2 - y1 / x2 - x1

-2 - 1 / -7 - (-3)  ---> this gives us -3 / -4 or simply 3/4. So our slope for line 1 is 3/4.

Now using the formula, (y - y1) = m (x - x1) we find the line.

(y - 1) = 3/4 (x - (-3)) ---> (y - 1) = 3/4x + 9/4.

Now we add one to each side to get y = 3/4x + 13/4.

Now for line 2, we use the same process and formulas.

Find the slope of line 2.

4 - (-1) / 8 - 2 gives us 5/6. Our slope for line 2 is 5/6.

(y - (-1)) = 5/6 (x - 2).

(y + 1) = 5/6x - 5/3 ---> now subtract one from both sides to get...

y = 5/6x - 8/3.

Since the two lines do not have the same slope or the negative reciprocal of one slope being the other, the two lines through the given points are neither parallel nor are they perpendicular.

NEITHER  

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.