Final answer:
A line with a slope of 1/3 passes through point P(0,1) and point A(0,1). To find a third point, substitute the coordinates of any of the other given points into the equation y = (1/3)x + 1 and check if it satisfies the equation.
Step-by-step explanation:
In order to find the points, we need to use the point-slope formula: y - y1 = m(x - x1). Given that the slope is 1/3, we can choose any three of the given points and substitute their coordinates as (x1, y1) in the formula. Let's use point P(0,1) and point A(0,1):
For point P(0,1): y - 1 = (1/3)(x - 0)
y = (1/3)x + 1
For point A(0,1): 1 - 1 = (1/3)(0 - 0)
0 = 0
We can see that both point P and point A satisfy the equation y = (1/3)x + 1. Therefore, the line with a slope of 1/3 passes through point P and point A. Another point that the line passes through can be found by substituting the coordinates of any of the other given points into the equation and checking if it satisfies the equation.