Final answer:
The point (-9, 9) is not on the graph of the function f(x) = y = 9 + 3x. Substituting x = -9 into the equation gives a y-value of -18. Another point with a y-value of 9 on this line would be the y-intercept, which is (0, 9).
Step-by-step explanation:
The student is inquiring whether the point (-9, 9) lies on the graph of the function f(x) = y = 9 + 3x. To determine if a point is on a graph, we can substitute the x-coordinate into the equation and see if the resulting y-value matches the y-coordinate of the point in question. Substituting x = -9, we obtain y = 9 + 3(-9) = 9 - 27 = -18, which does not match the y-coordinate of the point (-9, 9). Therefore, the point (-9, 9) is not on the graph of the given function. However, for a point to have the same y-value as the given y-coordinate, which is 9, we can set y = 9 in the original equation and solve for x: y = 9 + 3x implies that 9 = 9 + 3x; subtracting 9 from both sides, we have 0 = 3x; therefore, x = 0. Thus, the point with the same y-value of 9 is (0, 9), which is also the y-intercept of the line.