Question

How could you write the equation of a line that would be parallel to y=−3x−2
𝑦
=
−
3
𝑥
−
2
but not share any points?(1 point)
Responses

y=−3x−2
𝑦
=
−
3
𝑥
−
2
y equals negative 3 x minus 2

y=3x−2
𝑦
=
3
𝑥
−
2
y equals 3 x minus 2

y=−3x+8
𝑦
=
−
3
𝑥
+
8
y equals negative 3 x plus 8

y=3x+8

Answer 1

To write the equation of a line that is parallel to the given line \(y = -3x - 2\), you need to ensure it has the same slope. The slope of the given line is \(-3\).

For the new line to be parallel and not share any points with the original line, it must be a different y-intercept.

Among the provided options, the equation that maintains the same slope of \(-3\) but has a different y-intercept is:

**\(y = -3x + 8\)**

This line is parallel to \(y = -3x - 2\) (same slope) but will not intersect it (different y-intercept).

So the response is:
**y = -3x + 8**