What is the equation of a line that passes through the point (-3,7) and is perpendicular to the line 2y+6x=12
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
so
The given line is
2y+6x=12
step 1
Find the slope
isolate the variable y
2y=-6x+12
y=-3x+6
the slope is m=-3
therefore
the slope of teh perpendicular line is
m=1/3
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=1/3
(x1,y1)=(-3,7)
substitute
y-7=(1/3)(x+3)
convert to slope intercept form
isolate the variable y
y-7=(1/3)x+1
y=(1/3)x+8