Which BEST describes the relationship between the lines with equations $$ -4 x+2 y=-5 $$ and $$ -8 x+4 y=0 $$ ? A. neither parallel nor perpendicular B. perpendicular C. parallel D. same line

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To determine the relationship between the two lines given by the equations:

1. $$ -4x + 2y = -5 $$
2. $$ -8x + 4y = 0 $$

**Step 1: Find the slopes of both lines.**

First, rewrite both equations in the slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope.

**For the first line:**
$$
-4x + 2y = -5 \
2y = 4x - 5 \
y = 2x - \frac{5}{2}
$$
So, the slope $$ m_1 = 2 $$.

**For the second line:**
$$
-8x + 4y = 0 \
4y = 8x \
y = 2x
$$
So, the slope $$ m_2 = 2 $$.

**Step 2: Compare the slopes.**

Both lines have the same slope ($$ m_1 = m_2 = 2 $$), which means they are either **parallel** or **the same line**.

**Step 3: Check if they are the same line.**

To determine if they are the same line, see if one equation is a multiple of the other.

Multiplying the first equation by 2:
$$
2(-4x + 2y) = 2(-5) \
-8x + 4y = -10
$$
This is not the same as the second equation ($$ -8x + 4y = 0 $$), so they are **not** the same line.

**Conclusion:**

Since the lines have the same slope but are not the same line, they are **parallel**.

**Answer:**  
C. parallel
The lines are parallel.

Which BEST describes the relationship between the lines with equations \( -4 x+2 y=-5 \) and \( -8 x+4 y=0 \) ? A. neither parallel nor perpendicular B. perpendicular C. parallel D. same line

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