Final answer:
The slope of a line tells us its steepness and direction but cannot determine a single coordinate without additional information such as a specific point or the y-intercept. Therefore, option (d) Slope cannot determine a single coordinate is the correct answer.
Step-by-step explanation:
To find a coordinate on a line given a slope, you must have an initial point and the slope of the line. Since the slope represents how much the y-coordinate changes for a unit change in the x-coordinate, each pair of coordinates provided in the options (a) (0, 0), (b) (1, 1), and (c) (2, 2) represents points on a line with a slope of 1. This is because, for each option, as the x-coordinate increases by 1, the y-coordinate also increases by 1, which is characteristic of a slope of 1.
However, the slope itself does not determine a single specific coordinate on a line; it only tells us the steepness and direction of the line. Without additional information, such as a specific point on the line (other than the ones given) or the y-intercept, we cannot determine a unique point based solely on the slope value. Therefore, the mention correct option in the final answer is (d) Slope cannot determine a single coordinate.
The concept of slope is fundamental in algebra and is often visualized on a graph where it represents the rise over run between two points on a straight line. The rise refers to the change in the y-value, and the run refers to the change in the x-value. In a mathematical formula, slope (m) is calculated as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of two distinct points on the line.