Find the slopes of the lines that passes through the given points. Then determine if the two lines are parallel or perpendicular or neither.

Question

The line passing through the points (8,5) and (7,3).
The line passing through the points (6,-8) and (4,-7).
The slope of line 1 is
Response area
and the slope of line 2 is
Response area
. These lines are
Response area
.
m=
−2
−2NeitherPerpendicularm=
1
2
12m=
2
2m=
−
1
2
−12Parallel

Answer 1

To determine the slopes of the lines based on the given points, we can use the slope formula:

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

Line 1: Points (8, 5) and (7, 3)

Let \( (x_1, y_1) = (8, 5) \) and \( (x_2, y_2) = (7, 3) \).

Plugging in the points:

\[ m_1 = \frac{3 - 5}{7 - 8} = \frac{-2}{-1} = 2 \]

Line 2: Points (6, -8) and (4, -7)

Let \( (x_1, y_1) = (6, -8) \) and \( (x_2, y_2) = (4, -7) \).

Plugging in the points:

\[ m_2 = \frac{-7 - (-8)}{4 - 6} = \frac{-7 + 8}{4 - 6} = \frac{1}{-2} = -\frac{1}{2} \]

Summary of Slopes

• The slope of line 1 is \( m_1 = 2 \)
• The slope of line 2 is \( m_2 = -\frac{1}{2} \)

Determining Relationship Between the Lines

To check if the lines are parallel, perpendicular, or neither:

• Parallel lines have equal slopes.
• Perpendicular lines have slopes that are negative reciprocals of each other. For two slopes \(m_1\) and \(m_2\), this means \(m_1 \times m_2 = -1\).

Calculating the product:

\[ m_1 \times m_2 = 2 \times \left(-\frac{1}{2}\right) = -1 \]

Since the product of the slopes is \(-1\), the two lines are perpendicular.

Final Response

• The slope of line 1 is 2.
• The slope of line 2 is -1/2.
• These lines are perpendicular.