Final answer:
The equation that represents the line passing through the points (-3, 7) and (9, -1) is y = -2/3x + 5. This is achieved by finding the slope of the line and applying the point-slope formula using one of the points to get the equation in slope-intercept form.
Step-by-step explanation:
The equation of the line passing through the points (-3, 7) and (9, -1) can be found by calculating the slope (m) and using the point-slope form of the equation of a line. The slope is calculated as:
m = (y2 - y1) / (x2 - x1) = (-1 - 7) / (9 - (-3)) = -8 / 12 = -2 / 3
Using one of the points (-3, 7) and the slope we can plug them into the point-slope formula: y - y1 = m(x - x1). This gives us:
y - 7 = (-2 / 3)(x - (-3))
Expanding and simplifying, we get: y = (-2 / 3)x - 2 + 7
Finally, y = (-2 / 3)x + 5, which matches option A.