Which equation represents a line which is perpendicular to the line 6x +y = -4?
step 1
Find the slope of the given line
we have
6x+y=-4
isolate the avriable y
so
y=-6x-4
the slope is m=-6
step 2
Find the slope of the perpendicular line to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is
m=1/6
therefore
the slope of the perpendicular line must be equal to m=1/6
the answer is
y=1/6x+8