Questions: Oct 17 Take Quiz Question 10 Here again are the equations from the previous question. Equation 1: 5x-2y+0=12 Equation 2: 2y+5y=14 Based on the slopes you found in the previous question, what do you know about the lines? If you need it, here is a sheet of graph grid (opens in a new tab). The lines are parallel. The lines are perpendicular. The lines are neither parallel nor perpendicular. Quiz saved at 8:38am

Solution Steps

To determine the relationship between the lines, we need to find the slopes of the given equations. The general form of a linear equation is \(Ax + By = C\). We can convert each equation to the slope-intercept form \(y = mx + b\), where \(m\) is the slope. Once we have the slopes, we can compare them to determine if the lines are parallel, perpendicular, or neither.

We have the following equations:

1. \( 5x - 2y = 12 \)
2. \( 7y = 14 \)

To find the slopes, we will rearrange each equation into the slope-intercept form \( y = mx + b \).

For the first equation: \[ 5x - 2y = 12 \implies -2y = -5x + 12 \implies y = \frac{5}{2}x - 6 \] Thus, the slope \( m_1 = \frac{5}{2} \).

For the second equation: \[ 7y = 14 \implies y = 2 \] This indicates that the slope \( m_2 = 0 \).

Now we compare the slopes:

• \( m_1 = \frac{5}{2} \)
• \( m_2 = 0 \)

Since \( m_1 \neq m_2 \) and \( m_1 \) is not equal to \(-1 \times m_2\), the lines are neither parallel nor perpendicular.

Final Answer