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−2
y equals 3 x minus 2

y=−3x−2
y equals negative 3 x minus 2

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

y=−3x+8

Answer 1

To write the equation of a line that is parallel to the given line \( y = -3x - 2 \), we need to maintain 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 can choose a different y-intercept.

The equation of a line in slope-intercept form is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. In this case, we need the slope \( m = -3 \) and any y-intercept \( b \) that is different from \(-2\).

Among the options provided, the line \( y = -3x + 8 \) has the same slope of \(-3\) but a different y-intercept (+8). Therefore, it will be parallel and not share any points with the original line.

So, the correct answer is:

**y = -3x + 8**