Final answer:
To find the equation of a line that is parallel to a given line and passes through a given point, we use the point-slope form of a linear equation. In this case, plugging in the values for the point (2,7) and the slope -1/3 gives us the equation y = (-1/3)x + (23/3). Therefore, the correct equation is Option B.
Step-by-step explanation:
To find the equation of a line that is parallel to the line defined by x+3y=9 and passes through the point (2,7), we need to determine the slope of the given line. The given equation can be rewritten in slope-intercept form as y = (-1/3)x + 3. Since parallel lines have equal slopes, the slope of the desired line is also -1/3. We can then use the point-slope form of a linear equation to find the equation of the desired line:
y - y1 = m(x - x1)
Plugging in the values for the point (2,7) and the slope -1/3, we get:
y - 7 = (-1/3)(x - 2)
Expanding and rearranging the equation:
y = (-1/3)x + (2/3) + 7
y = (-1/3)x + (23/3)
Therefore, the equation of the line that passes through the point (2,7) and is parallel to the line x+3y=9 is y = (-1/3)x + (23/3) (Option B).