Question

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Find the slopes of the lines that passes through the given points. Then determine if the two lines are parallel or perpendicular or neither.
The line passing through the points (2,-5) and (6,2).
The line passing through the points (4,-3) and (8,4).
The slope of line 1 is
Response area
and the slope of line 2 is
Response area
. These lines are
Response area
.
m=
−
4
7
−47NeitherPerpendicularm=
7
4
74m=
4
7
47m=
−
7
4
−74Parallel

Answer 1

To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

**1. Finding the slope for line 1:**

The points are (2, -5) and (6, 2).

\[
m_1 = \frac{2 - (-5)}{6 - 2} = \frac{2 + 5}{6 - 2} = \frac{7}{4}
\]

**2. Finding the slope for line 2:**

The points are (4, -3) and (8, 4).

\[
m_2 = \frac{4 - (-3)}{8 - 4} = \frac{4 + 3}{8 - 4} = \frac{7}{4}
\]

Now, we have:
- The slope of line 1: \(m_1 = \frac{7}{4}\)
- The slope of line 2: \(m_2 = \frac{7}{4}\)

Since both slopes are equal, the lines are **parallel**.

Here are the responses to insert:

The slope of line 1 is **\(\frac{7}{4}\)** and the slope of line 2 is **\(\frac{7}{4}\)**. These lines are **parallel**.