Final answer:
After substituting the x-values of the given options into the point-slope form equation y - 10 = 3(x - 11), only option D (3, -14) results in a y-value that matches the one given in the option, making it the only point that falls on the line.
Step-by-step explanation:
To determine which points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11), we can plug in the x-values from each option to see if the resulting y-value matches those given in the options.
- For option A (-2, -17), plug in x = -2: y - 10 = 3(-2 - 11) → y - 10 = 3(-13) → y - 10 = -39 → y = -29, which does not match the y-value of -17.
- For option B (1, 21), plug in x = 1: y - 10 = 3(1 - 11) → y - 10 = 3(-10) → y - 10 = -30 → y = -20, which does not match the y-value of 21.
- For option C (1, -21), the calculation is the same as for B, and it does not match.
- For option D (3, -14), plug in x = 3: y - 10 = 3(3 - 11) → y - 10 = 3(-8) → y - 10 = -24 → y = -14, which matches the y-value of -14.
Therefore, the correct option is D. (3, -14).