Sure, let's solve this step-by-step:
1. Transform the first equation to slope-intercept form (y = mx + b)
- Start with the given equation: [tex]\(6x - 2y = -2\)[/tex]
- Solve for [tex]\(y\)[/tex]:
- Subtract [tex]\(6x\)[/tex] from both sides: [tex]\(-2y = -6x - 2\)[/tex]
- Divide every term by [tex]\(-2\)[/tex]: [tex]\( y = 3x + 1\)[/tex]
2. Identify the slope of both equations
- For the first equation [tex]\(y = 3x + 1\)[/tex], the slope ([tex]\(m\)[/tex]) is 3.
- The second equation is already in slope-intercept form [tex]\(y = 3x + 12\)[/tex]. The slope ([tex]\(m\)[/tex]) is 3.
3. Compare the slopes to determine the relationship between both lines
- The slope of the first line is [tex]\(3\)[/tex].
- The slope of the second line is [tex]\(3\)[/tex].
4. Determine if the lines are parallel or perpendicular
- Two lines are parallel if their slopes are equal.
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
5. Calculate the product of the slopes
- Product of the slopes: [tex]\(3 \times 3 = 9\)[/tex]
6. Conclusion
- The product of the slopes is [tex]\(9\)[/tex], not [tex]\(-1\)[/tex], so the lines are not perpendicular.
- Since both slopes are [tex]\(3\)[/tex], the lines are parallel.
### Select the correct answer from each drop-down menu:
Are these lines perpendicular, parallel, or neither based off their slopes?
The product of their slopes is [tex]\(9\)[/tex], so the lines are parallel.
