Final answer:
The equation of the secant line passing through (-3, g(-3)) and (5, g(5)) is y = -7x + 57.
Step-by-step explanation:
The equation of a secant line passing through two points, (-3, g(-3)) and (5, g(5)), can be found by using the slope formula. The slope of the secant line is given by the difference in y-coordinates divided by the difference in x-coordinates. We can find the y-coordinates by plugging the given x-values into the function g(x).
For (-3, g(-3)): g(-3) = (-3)^2 - 9(-3) = 9 + 27 = 36
For (5, g(5)): g(5) = (5)^2 - 9(5) = 25 - 45 = -20
Using the coordinates (-3, 36) and (5, -20), we can calculate the slope of the secant line: m = (y2 - y1) / (x2 - x1) = (-20 - 36) / (5 - (-3)) = -56 / 8 = -7.
Therefore, the equation of the secant line passing through (-3, g(-3)) and (5, g(5)) is: y = -7x + b. To find the y-intercept, b, we can plug in the coordinates of one of the given points. Let's use (-3, 36): 36 = -7(-3) + b, b = 57.
The equation of the secant line is y = -7x + 57.