Which of the following equations represents a line that passes through the points (6, -9) and (2, 1)?
1. y -1 = -5(x - 2)
II. y = -x + 6
Neither
I only
II only
I and ll only

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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