Question

Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses

No…these lines are parallel
No…these lines are parallel

No…these lines are perpendicular
No…these lines are perpendicular

Yes…these lines are parallel
Yes…these lines are parallel

You cannot tell without a graph
You cannot tell without a graph

Yes…these lines are perpendicular
Yes…these lines are perpendicular

Yes…these lines are not parallel
Yes…these lines are not parallel

Answer 1

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**.