Final answer:
The equation of the line parallel to y = 1/2x + 14 and passing through the point (6, 9) is y = 1/2x + 6, with the same slope of 1/2 and a calculated y-intercept of 6.
Step-by-step explanation:
To find the equation of a line that is parallel to another and that passes through a given point, you need to follow a couple of steps. The line y = 1/2x + 14 has a slope (m) of 1/2. Any line parallel to this one will also have the same slope. The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since the new line must pass through the point (6, 9) and has the same slope as the given line, you can substitute the slope and the point into the equation to find b:
Using the point (6, 9):
9 = (1/2) * 6 + b
9 = 3 + b
b = 9 - 3
b = 6
Therefore, the equation of the line that is parallel to y = 1/2x + 14 and passes through the point (6, 9) is y = 1/2x + 6.