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 3 x plus 8
y=3x−2
y equals 3 x minus 2
y=−3x+8
y equals negative 3 x plus 8
y=−3x−2
but not share any points?(1 point)
Responses
y=3x+8
y equals 3 x plus 8
y=3x−2
y equals 3 x minus 2
y=−3x+8
y equals negative 3 x plus 8
y=−3x−2
Answers
GPT-4o mini
To write the equation of a line that is parallel to \(y = -3x - 2\), you need to keep the same slope. The slope of the given line is \(-3\). Any line parallel to it will also have this slope. Therefore, the general form of the equation for the parallel line will be:
\[ y = -3x + b \]
where \(b\) is a constant. To ensure that the parallel line does not share any points with the original line, \(b\) must be different from \(-2\), which is the y-intercept of the original line.
Among the options provided, the only equation that retains the correct slope of \(-3\) and has a different y-intercept from the original line is:
**y = -3x + 8**
This line is parallel to \(y = -3x - 2\) and does not share any points because the y-intercept (8) is different from -2.
So, the final answer is:
**\(y = -3x + 8\)**
\[ y = -3x + b \]
where \(b\) is a constant. To ensure that the parallel line does not share any points with the original line, \(b\) must be different from \(-2\), which is the y-intercept of the original line.
Among the options provided, the only equation that retains the correct slope of \(-3\) and has a different y-intercept from the original line is:
**y = -3x + 8**
This line is parallel to \(y = -3x - 2\) and does not share any points because the y-intercept (8) is different from -2.
So, the final answer is:
**\(y = -3x + 8\)**