Questions: For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither. 8 x-6 y=4 8 x+12 y=-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of 8 x-6 y=4 is In. (Type an integer or a simplified fraction.) B. The slope of 8 x-6 y=4 is undefined.

Solution Steps

For the first equation \( 8x - 6y = 4 \), we rearrange it into slope-intercept form \( y = mx + b \):

\[ -6y = -8x + 4 \implies y = \frac{4}{6}x - \frac{4}{6} = \frac{2}{3}x - \frac{2}{3} \]

Thus, the slope \( m_1 \) is:

\[ m_1 = \frac{4}{6} = \frac{2}{3} \]

For the second equation \( 8x + 12y = -1 \), we also rearrange it:

\[ 12y = -8x - 1 \implies y = -\frac{8}{12}x - \frac{1}{12} = -\frac{2}{3}x - \frac{1}{12} \]

Thus, the slope \( m_2 \) is:

\[ m_2 = -\frac{2}{3} \]

To determine the relationship between the two lines, we compare their slopes:

• The slopes are \( m_1 = \frac{2}{3} \) and \( m_2 = -\frac{2}{3} \).
• Since \( m_1 \cdot m_2 = \frac{2}{3} \cdot -\frac{2}{3} = -\frac{4}{9} \), which is not equal to -1, the lines are neither parallel nor perpendicular.

Final Answer