To determine whether the two lines represented by the points (-6, -10) and (4, -2) are parallel, perpendicular, or neither, we first need to calculate the slope of the line that passes through these two points.
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let’s assign the points:
- Point 1 \((x_1, y_1) = (-6, -10)\)
- Point 2 \((x_2, y_2) = (4, -2)\)
Now, we can substitute the coordinates into the slope formula:
\[ m = \frac{-2 - (-10)}{4 - (-6)} \]
Calculating the numerator:
\[ -2 - (-10) = -2 + 10 = 8 \]
Calculating the denominator:
\[ 4 - (-6) = 4 + 6 = 10 \]
Now plugging these values back into the slope formula:
\[ m = \frac{8}{10} = \frac{4}{5} \]
Next, we need to check the slopes of the two lines represented by these points. Since we are only given one line with these two points, we can only analyze its slope further.
To determine if two lines are parallel or perpendicular, we would generally need the slope of a second line and compare their slopes:
- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals of each other (i.e. \(m_1 \cdot m_2 = -1\)).
Since we only have one line with a slope of \(\frac{4}{5}\), we cannot conclude anything definitive about parallelism or perpendicularity without a second line.
Thus, the relation between this single line and a second line depends on further information about that second line. If you have a specific second line or points, please provide, and we can determine the relationships accurately.
In summary, based on the provided points, we have a single line with slope \(\frac{4}{5}\), and we cannot conclude whether this line is parallel or perpendicular to another without additional information.