Final answer:
After calculating the slope of the line that passes through points E(-2, 2) and F(5, 1), the equation is found to be y = -1/7x + 12/7. None of the given answer choices perfectly match the determined equation, but the closest one considering just the slope is C) y = -1/7x - 3/7.
Step-by-step explanation:
To determine which of the given options is the equation of the line passing through points E(-2, 2) and F(5, 1), we first need to calculate the slope (m) of the line. The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of E and F, we get:
m = (1 - 2) / (5 - (-2))
m = (-1) / (7)
m = -1/7
With the slope known, we can use point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Using point E(-2, 2), the equation becomes:
y - 2 = -1/7(x - (-2))
y - 2 = -1/7x - 2/7
y = -1/7x - 2/7 + 2
y = -1/7x + 14/7 - 2/7
y = -1/7x + 12/7
Converting 12/7 to a decimal, we get:
y = -1/7x + 1.714...
None of the answer choices exactly match this equation, indicating a possible error in the question or answer choices. However, the closest answer, when only considering the slope, would be:
C) y = -1/7x - 3/7