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 negative 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 negative 3 x minus 2
y=−3x+8
y equals negative 3 x plus 8
y=3x−2
Answers
GPT-4o mini
To find a line that is parallel to the line given by the equation \( y = -3x - 2 \), we need a line with the same slope. The slope of the given line is \(-3\).
To ensure that the new line does not share any points with the original line, we need to choose a different y-intercept. The y-intercept of the original line is \(-2\). If we select a different y-intercept, we will have a parallel line that does not intersect the original line.
Among the given options, the equation \( y = -3x + 8 \) has the same slope of \(-3\) but a different y-intercept (8 instead of -2).
Therefore, the equation of a line that is parallel to \( y = -3x - 2 \) but does not share any points is:
**y = -3x + 8**
To ensure that the new line does not share any points with the original line, we need to choose a different y-intercept. The y-intercept of the original line is \(-2\). If we select a different y-intercept, we will have a parallel line that does not intersect the original line.
Among the given options, the equation \( y = -3x + 8 \) has the same slope of \(-3\) but a different y-intercept (8 instead of -2).
Therefore, the equation of a line that is parallel to \( y = -3x - 2 \) but does not share any points is:
**y = -3x + 8**