To determine whether the equations contain the given points, (6, -9) and (2, 1) is by plugging in their values into the equation to see if they will provide a true statement.
For the first equation, y - 1 = -5(x - 2):
Transform into slope-intercept form, y = mx + b:
y - 1 = -5(x - 2)
y - 1 = -5x + 10
Add 1 to both sides to isolate y:
y - 1 + 1 = -5x + 10 + 1
y = -5x + 11 (this is the slope-intercept form).
Now, we must substitute both points into the equation to see if they will provide a true statement:
y = -5x + 11
Test point (6, -9)
y = -5x + 11
-9 = -5(6) + 11
-9 = -30 + 11
-9 = -19 (false statement).
Test point (2, 1):
y = -5x + 11
1 = -5(2) + 11
1 = -10 + 11
1 = 1 (True statement).
Test both points in the y = -x + 6
(6, -9):
-9 = -(6) + 6
-9 = -6 + 6
-9 = 0 (false statement).
(2, 1):
1 = -(2) + 6
1 = -2 + 6
1 = 4 (false statement).
Therefore, the correct answer is NEITHER.
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