Determine if this line is parallel perpendicular or neither

Question

Y=3x-7
Y=3x+1

Answer 1

To determine if the two lines are parallel, perpendicular, or neither, we need to look at their slopes.

The equations are given in slope-intercept form \( y = mx + b \), where \( m \) represents the slope.

1. For the first line \( Y = 3x - 7 \):

   • The slope \( m_1 = 3 \).

2. For the second line \( Y = 3x + 1 \):

   • The slope \( m_2 = 3 \).

Since both lines have the same slope (\( m_1 = m_2 = 3 \)), they are parallel.

Thus, the two lines are parallel.

Answer 2

Y= -2/5x + 3
Y = 2/5 x + 8

Answer 3

To determine if the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The equations are given in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

1. For the first line \( Y = -\frac{2}{5}x + 3 \):

   • The slope \( m_1 = -\frac{2}{5} \).

2. For the second line \( Y = \frac{2}{5}x + 8 \):

   • The slope \( m_2 = \frac{2}{5} \).

Next, we check the relationship between the slopes:

• Parallel lines have the same slope, i.e., \( m_1 = m_2 \).
• Perpendicular lines have slopes that are negative reciprocals of each other, i.e., \( m_1 \cdot m_2 = -1 \).

In this case:

• \( m_1 = -\frac{2}{5} \)
• \( m_2 = \frac{2}{5} \)

To check if they are perpendicular: \[ m_1 \cdot m_2 = -\frac{2}{5} \cdot \frac{2}{5} = -\frac{4}{25} \neq -1 \]

Since the slopes are not equal and they are not negative reciprocals of each other, the lines are neither parallel nor perpendicular.