Question

Decide which of the two points lies on the graph of the line.

1. X + Y = 8
A. (2,4) B. (2,6)

2. X = 4
A.(4,2) B. (2,4)

3. Y = X - 2
A. (4,6) B. (6,4)

Answer 1

Answers:

1. B) (2,6)
2. A) (4,2)
3. B) (6,4)

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Explanations:

1. For this problem, the x and y coordinates must add to 8. In choice A, we have x+y = 2+4 = 6, which doesn't work. But choice B does work since x+y = 2+6 = 8. Therefore, the point (2,6) is located on the line x+y = 8. The equation x+y = 8 is equivalent to y = -x+8.
2. The x coordinate must be equal to 4. The y coordinate can be anything you want. The point (4,2) is on this line, while (2,4) is not. Another point on this line is (4,1). The line is completely vertical.
3. If we plugged the x & y coordinates of choice A into the equation, we get 6 = 4-2 which then becomes 6 = 2 and that's a false statement. That rules out choice A. If we try choice B, then we get 4 = 6-2 which becomes 4 = 4. We get a true statement so choice B is the answer.