Remember that
If two lines are parallel, then their slopes are equal
so
Part a
line passes through the point (5,-6)
and is parallel to 2x+y=12
Find the slope of the given line
isolate the vaiable y
y=-2x+12
m=-2
Find the equation of the parallel line in slope intercept form
y=mx+b
we have
m=-2
point (5,-6)
substitute
-6=-2(5)+b
b=10-6
b=4
therefore
y=-2x+4
Part b
we have
3x+5y=7
isolate the variable y
5y=-3x+7
y=(-3/5)x+7/5
m=-3/5
Find the equation of the parallel line in slope intercept form
y=mx+b
we have
m=-3/5
point (5,-6)
substitute
-6=(-3/5)(5)+b
b=-6+3
b=-3
therefore
y=(-3/5)x-3
Part c
we have
x+3y=8
3y=-x+8
y=(-1/3)x+8/3
m=-1/3
Find the equation of the parallel line in slope intercept form
y=mx+b
we have
m=-1/3
point (5,-6)
substitute
-6=(-1/3)(5)+b
b=-6+5/3
b=-13/3
therefore
y=(-1/3)x-13/3
Part d
we have
7x-12y=5
12y=7x-5
y=(7/12)x-5/12
m=7/12
Find the equation of the parallel line in slope intercept form
y=mx+b
we have
m=7/12
point (5,-6)
substitute
-6=(7/12)(5)+b
b=-6-35/12
b=37/12
therefore
y=(7/12)x+37/12
Part e
we have
x=7
Its a vertical line
the slope is undefined
so
the parallel line is
x=5 because passes through the point (5,-6)
Part f
we so
the parall