Question
Which line is parallel to the line y = − x − 5 and goes through the point ? (1 point)
3
2
(0, 2)
y = − x
3
2
y = − x + 2
3
2
3y = −2x − 15
y = − (x + 10/3)
3
2
(0, 2)
y = − x
3
2
y = − x + 2
3
2
3y = −2x − 15
y = − (x + 10/3)
Answers
GPT-4o mini
To find a line that is parallel to the original line \(y = -x - 5\), we need to determine the slope of this line. The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope.
From the equation \(y = -x - 5\), we see that the slope \(m = -1\).
Lines that are parallel have the same slope, so a parallel line will also have a slope of \(-1\).
Now we need to determine which of the provided equations goes through a specific point. However, it seems that the point through which the parallel line must pass is not provided in your question.
Given the options:
1. \(y = -x\)
2. \(y = -x + 2\)
3. \(3y = -2x - 15\) (this needs to be rewritten in slope-intercept form)
4. \(y = - (x + 10/3)\) (which simplifies to \(y = -x - 10/3\))
Let's analyze these equations:
1. **\(y = -x\)**: This has a slope of \(-1\).
2. **\(y = -x + 2\)**: This also has a slope of \(-1\).
3. **\(3y = -2x - 15\)**: Dividing by 3, we have \(y = -\frac{2}{3}x - 5\). The slope is \(-\frac{2}{3}\), so this is not parallel.
4. **\(y = - (x + 10/3)\)**: This simplifies to \(y = -x - \frac{10}{3}\), with a slope of \(-1\), making it parallel.
So, the lines that are parallel to \(y = -x - 5\) are:
- \(y = -x\)
- \(y = -x + 2\)
- \(y = - (x + 10/3)\)
However, without the specific point that the parallel line must pass through, we cannot choose definitively between these options. If you provide the specific point, we can determine which equation goes through that point.
From the equation \(y = -x - 5\), we see that the slope \(m = -1\).
Lines that are parallel have the same slope, so a parallel line will also have a slope of \(-1\).
Now we need to determine which of the provided equations goes through a specific point. However, it seems that the point through which the parallel line must pass is not provided in your question.
Given the options:
1. \(y = -x\)
2. \(y = -x + 2\)
3. \(3y = -2x - 15\) (this needs to be rewritten in slope-intercept form)
4. \(y = - (x + 10/3)\) (which simplifies to \(y = -x - 10/3\))
Let's analyze these equations:
1. **\(y = -x\)**: This has a slope of \(-1\).
2. **\(y = -x + 2\)**: This also has a slope of \(-1\).
3. **\(3y = -2x - 15\)**: Dividing by 3, we have \(y = -\frac{2}{3}x - 5\). The slope is \(-\frac{2}{3}\), so this is not parallel.
4. **\(y = - (x + 10/3)\)**: This simplifies to \(y = -x - \frac{10}{3}\), with a slope of \(-1\), making it parallel.
So, the lines that are parallel to \(y = -x - 5\) are:
- \(y = -x\)
- \(y = -x + 2\)
- \(y = - (x + 10/3)\)
However, without the specific point that the parallel line must pass through, we cannot choose definitively between these options. If you provide the specific point, we can determine which equation goes through that point.