O
undefined
0-3
о
3
о
0
The problem asks for the slope of a line passing through the points \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (2, 6)\). The slope of a line is defined as the measure of its steepness and direction, represented by the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on the line.
To calculate the slope \(m\), we use the slope formula:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points on the line. Here, we have \(x_1 = 0, y_1 = 0\) and \(x_2 = 2, y_2 = 6\). Substituting these values into the formula:
\[m = \frac{6 - 0}{2 - 0}\]
\[m = \frac{6}{2}\]
\[m = 3\]
Thus, the slope of the line is \(3\).
The calculated slope is \(3\). Comparing this result with the provided options, we see that it corresponds to the second option. Hence, the slope of the line through the points \((0, 0)\) and \((2, 6)\) is \(\boxed{3}\).
In civil engineering, determining the slope is essential for tasks like designing roads or ramps to ensure they are safe and accessible. For instance, if a wheelchair ramp needs to climb a height of 6 units over a horizontal distance of 2 units, the slope would be 3. This indicates how steep the incline is, which is crucial for compliance with safety standards and architectural planning.