To analyze the slopes of the lines, we first need to identify how to calculate the slope of a line given two points.
The slope \( m \) of a line between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this scenario, let's consider the line from the origin \((0, 0)\) to the point \((1, 4)\). We can use the slope formula:
- Points: \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (1, 4)\)
\[ m = \frac{4 - 0}{1 - 0} = \frac{4}{1} = 4 \]
Next, let's define the other line. Since the question mentions an alien stranded at the starting location, it implies we have another point, which is not specifically defined but for the sake of argument, let's assume the alien is at the starting point (e.g., another point at the origin).
If we draw a line from the origin to the point where the alien is (let’s assume to point \( (0, y) \)), this would not be a typical slope scenario since a point at the same vertical line would result in no horizontal movement, which means a vertical line.
If the line is vertical (i.e., from (0,0) to (0,y)), the slope is undefined because division by zero occurs.
Now when comparing:
- Slope of the line from \((0, 0)\) to \((1, 4)\) is \( 4 \).
- Slope of the line if it were vertical (no movement horizontally) is undefined.
Since we have one line with a specific slope and another that is vertical with an undefined slope, we can summarize:
- They are neither the same, nor opposites, nor reciprocals.
- The second line has no slope (specifically, it is undefined).
Therefore, the correct answer to the question is:
The second line has no slope.
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