Final answer:
The point-slope form of the equation is y - 7 = -1/3(x + 9).
Step-by-step explanation:
The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Given the two points (-9,7) and (9,1), we can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (1 - 7) / (9 - (-9)) = -6 / 18 = -1/3.
Using the point-slope form, we choose one of the points, say (-9,7), and substitute the values into the equation: y - y1 = m(x - x1), which becomes y - 7 = -1/3(x - (-9)).
Simplifying, we have y - 7 = -1/3(x + 9).