Which BEST describes the relationship between the lines with equations and ?
A. neither parallel nor perpendicular
B. perpendicular
C. parallel
D. same line

Ask by Mccarthy Hodges. in the United States

Jan 24,2025

Question

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

UpStudy AI · Accepted Answer

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 and ?
A. neither parallel nor perpendicular
B. perpendicular
C. parallel
D. same line

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Which BEST describes the relationship between the lines with equations and ? A. neither parallel nor perpendicular B. perpendicular C. parallel D. same line