Final answer:
None of the provided points (0, 1), (2, 0), (-6, 5), or (3, -2) lie on the line represented by the equation 1/3x + 2/3y = 1. This is verified by substituting the coordinates of each point into the equation and confirming that the equation does not hold true for any of them.
Step-by-step explanation:
The student asked to locate a third point on the line defined by the equation 1/3x + 2/3y = 1 and verify whether the given points (a) (0, 1) (b) (2, 0) (c) (-6, 5) (d) (3, -2) are on this line. To check if a point lies on a line, we need to substitute the x and y values of the point into the line's equation and see if the equation holds true.
To verify (0, 1): Let's substitute x = 0 and y = 1 into the equation.
1/3(0) + 2/3(1) = 1/3(0) + 2/3 = 0 + 2/3 = 2/3, which is not equal to 1. Hence, point (a) is not on the line.
To verify (2, 0): Let's substitute x = 2 and y = 0 into the equation.
1/3(2) + 2/3(0) = 2/3 + 0 = 2/3, which is not equal to 1. Hence, point (b) is not on the line.
To verify (-6, 5): Let's substitute x = -6 and y = 5 into the equation.
1/3(-6) + 2/3(5) = -2 + 10/3 = -2 + 3.33, which does not equal 1. Hence point (c) is not on the line.
To verify (3, -2): Let's substitute x = 3 and y = -2 into the equation.
1/3(3) + 2/3(-2) = 1 - 4/3 = 1 - 1.33, which equals -0.33, not 1. Hence point (d) is not on the line.
None of the given points lies on the line represented by the equation 1/3x + 2/3y = 1