Final answer:
To see if a point falls on the line with the equation y - 10 = 3(x - 11), substitute the x-coordinate into the equation and solve for y. If the resulting y-coordinate matches that of the point, it lies on the line.
Step-by-step explanation:
The student asks which points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11) when graphed. To determine if a point lies on the line, it must satisfy the equation when its coordinates are substituted for x and y.
In point-slope form, the equation of a straight line is y - y1 = m(x - x1), where m represents the slope of the line, and (x1, y1) is a point the line passes through. For the line in question, the slope is 3 and the specific point it passes through is (11, 10). To check if a point is on the line, you would plug the x-value of the point into the equation and see if the y-value you calculate matches the y-value of the point.
For example, let's check if the point (12, 13) is on the line. We substitute x with 12 so we get y - 10 = 3(12 - 11). This simplifies to y - 10 = 3. Adding 10 to both sides, we find y = 13. Since this matches the y-coordinate given, the point (12, 13) lies on the line.