Question

which equation represents a line which is parallel to the line 5x + y = -6

Answer 1

Two lines are parallel if and only if their slopes are the same, that is:

$m_1=m_2$

To find the slope of the original line we write it in slope-intercept form.

$y=mx+b$

Then:

$\begin{gathered} 5x+y=-6 \\ y=-5x-6 \end{gathered}$

Comparing the two equations we notice that the slope of the line is -5.

Therefore the parallel line has equation:

$y=-5x-4$