To determine whether the two lines intersect, we need to find the slopes of both lines.
Line 1: Through points (3, 7) and (-2, -5)
The slope \( m_1 \) is calculated using the formula:
\[ m_1 = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates \( (x_1, y_1) = (3, 7) \) and \( (x_2, y_2) = (-2, -5) \):
\[ m_1 = \frac{-5 - 7}{-2 - 3} = \frac{-12}{-5} = \frac{12}{5} \]
Line 2: Through points (4, 8) and (10, -2)
Now we calculate the slope \( m_2 \):
\[ m_2 = \frac{-2 - 8}{10 - 4} = \frac{-10}{6} = \frac{-5}{3} \]
Now we can compare the slopes of the two lines:
- The slope of Line 1 is \( \frac{12}{5} \).
- The slope of Line 2 is \( \frac{-5}{3} \).
Since the slopes are different, the lines are not parallel and will intersect at some point.
Thus, the correct response is:
Yes…these lines are not parallel.