To find the slopes of the lines passing through the given points, we will use the formula for the slope \( m \) of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
1. Finding the slope of the line through points (2, -5) and (6, 2):
Here, \((x_1, y_1) = (2, -5)\) and \((x_2, y_2) = (6, 2)\).
Using the slope formula:
\[ m_1 = \frac{2 - (-5)}{6 - 2} = \frac{2 + 5}{6 - 2} = \frac{7}{4} \]
2. Finding the slope of the line through points (4, -3) and (8, 4):
Here, \((x_1, y_1) = (4, -3)\) and \((x_2, y_2) = (8, 4)\).
Using the slope formula:
\[ m_2 = \frac{4 - (-3)}{8 - 4} = \frac{4 + 3}{8 - 4} = \frac{7}{4} \]
Comparison of the slopes:
- The slope of the first line is \( m_1 = \frac{7}{4} \).
- The slope of the second line is \( m_2 = \frac{7}{4} \).
Since both lines have the same slope (\( m_1 = m_2 \)), we can conclude that the two lines are parallel.
Summary:
- Slope of the first line: \( \frac{7}{4} \)
- Slope of the second line: \( \frac{7}{4} \)
- Conclusion: The lines are parallel.
1 answer