To find the slopes of the lines that pass through the given points, we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
1. Finding the slope of the line passing through the points (8, 5) and (7, 3):
Let \((x_1, y_1) = (8, 5)\) and \((x_2, y_2) = (7, 3)\).
Using the slope formula:
\[ m_1 = \frac{3 - 5}{7 - 8} = \frac{-2}{-1} = 2 \]
So, the slope of line 1 is \(m_1 = 2\).
2. Finding the slope of the line passing through the points (6, -8) and (4, -7):
Let \((x_1, y_1) = (6, -8)\) and \((x_2, y_2) = (4, -7)\).
Using the slope formula:
\[ m_2 = \frac{-7 - (-8)}{4 - 6} = \frac{-7 + 8}{4 - 6} = \frac{1}{-2} = -\frac{1}{2} \]
So, the slope of line 2 is \(m_2 = -\frac{1}{2}\).
Comparison of the slopes:
- Are the lines parallel?: Two lines are parallel if their slopes are equal. Here, \(m_1 \neq m_2\), so the lines are not parallel.
- Are the lines perpendicular?: Two lines are perpendicular if the product of their slopes is \(-1\).
Calculating the product of the slopes:
\[ m_1 \cdot m_2 = 2 \cdot \left(-\frac{1}{2}\right) = -1 \]
Since this product is \(-1\), the lines are perpendicular.
To summarize:
- The slope of line 1 is 2.
- The slope of line 2 is -\frac{1}{2}.
- These lines are perpendicular.