Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Select the correct answer from each drop-down menu.

Are these lines perpendicular, parallel, or neither based on their slopes?

[tex]\[
\begin{array}{l}
6x - 2y = -2 \\
y = 3x + 12
\end{array}
\][/tex]

The [tex]$\square$[/tex] of their slopes is [tex]$\square$[/tex], so the lines are [tex]$\square$[/tex].

Sagot :

GinnyAnswer
Let's begin by identifying the slopes of each line.

### Step 1: Convert the First Equation to Slope-Intercept Form
The first equation is \( 6x - 2y = -2 \). To find the slope, we need to convert it to the slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

1. Start with the equation:
[tex]\[ 6x - 2y = -2 \][/tex]

2. Isolate the \( y \)-term by subtracting \( 6x \) from both sides:
[tex]\[ -2y = -6x - 2 \][/tex]

3. Divide everything by \(-2\) to solve for \( y \):
[tex]\[ y = 3x + 1 \][/tex]

So, the slope \( m_1 \) of the first line is \( 3 \).

### Step 2: Identify the Slope of the Second Line
The second equation is \( y = 3x + 12 \). This is already in slope-intercept form \( y = mx + b \), where the slope \( m_2 \) is \( 3 \).

### Step 3: Determine the Relationship Between the Slopes
We compare the slopes \( m_1 \) and \( m_2 \):

- \( m_1 = 3 \)
- \( m_2 = 3 \)

1. If the slopes are equal (\( m_1 = m_2 \)), then the lines are parallel.
2. If the product of the slopes is \(-1\) (i.e., \( m_1 \times m_2 = -1 \)), the lines are perpendicular.
3. Otherwise, the lines are neither parallel nor perpendicular.

Since the slopes are equal (\( 3 = 3 \)), the lines are parallel.

### Conclusion
The product of their slopes is \( 9 \), which we don't actually need to figure out since the comparison indicated that both slopes are equal. Therefore, the lines are parallel.

So, the correct selections are:
- The product of their slopes is 9 ,
- so the lines are parallel.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.