Question
How could you write the equation of a line that would be parallel to y=−3x−2 but not share any points?(1 point) Responses y=−3x+8 y equals negative 3 x plus 8 y=−3x−2 y equals negative 3 x minus 2 y=3x+8 y equals 3 x plus 8 y=3x−2
Answers
GPT-4o mini
To write the equation of a line that is parallel to \( y = -3x - 2 \), we need to use the same slope. The slope of the given line is \(-3\). A parallel line will also have this slope, so it can be written in the form \( y = -3x + b \) where \( b \) is a different y-intercept than \(-2\) in order to ensure they do not share any points.
Now, let's examine the given options:
1. \( y = -3x + 8 \)
2. \( y = -3x - 2 \)
3. \( y = 3x + 8 \)
4. \( y = 3x - 2 \)
Out of these, options 1 and 2 have a slope of \(-3\), but option 2 is the exact same line. Therefore, the only correct option that is parallel (same slope) but does not share any points is:
**\( y = -3x + 8 \)**
So the correct response is:
\( y = -3x + 8 \)
Now, let's examine the given options:
1. \( y = -3x + 8 \)
2. \( y = -3x - 2 \)
3. \( y = 3x + 8 \)
4. \( y = 3x - 2 \)
Out of these, options 1 and 2 have a slope of \(-3\), but option 2 is the exact same line. Therefore, the only correct option that is parallel (same slope) but does not share any points is:
**\( y = -3x + 8 \)**
So the correct response is:
\( y = -3x + 8 \)