In the xy-plane above, the circle has center (0, 0) and AB is a diameter of the circle. What is the equation of the line passing through points A and B?
y = 2/3 x is the equation of the line passing through points A and B.
Since AB is a diameter of the circle centered at (0, 0), the line through points A and B must pass through the origin. Given the slope of 2/3, this line rises 2 units for every 3 units it runs horizontally, making it the correct representation of the line connecting points A and B.
This equation represents a line with a negative slope, indicating that as x increases, y decreases. Since the points A and B are on a diameter of a circle that is centered at the origin, the line must have a positive slope, making this option incorrect.
This equation has a positive slope of 2/3, indicating that the line rises as it moves to the right. This is consistent with the line passing through the points A and B on the diameter of the circle, confirming that it is the correct choice.
This equation has a steeper positive slope of 3/2 compared to the correct answer. While it is a valid linear equation, it does not accurately describe the slope of the line connecting A and B, which rises at a rate of 2 units for every 3 units of horizontal distance.
This option represents a line with a very steep slope of 4, which implies it rises quickly compared to the line connecting points A and B. Therefore, this option does not match the required slope and is incorrect.
The equation of the line passing through points A and B on the diameter of the circle is y = 2/3 x. This line's slope accurately reflects the relationship between the coordinates of points A and B while maintaining the requirement that the line passes through the origin. The other choices either have incorrect slopes or negative slopes, failing to represent the line correctly.
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