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