Question

Select the equations that are parallel and perpendicular to y = 1/4x + 7 and that pass through the point (-8, 9).

Answer 1

parallel :
y=mx+b , m= 1/4 , ( -8.9)
9=1/4(-8)+b
8=-8/4+b
8=-2+b
10=b
y=1/4x+10

perpendicular:
y=mx+b , m= -4 , ( -8.9)
9=-4(-8)+b
9=32+b
-23=b
y=-4x-23

Answer 2

parallel lines equation
first of all we have to notice that parallel lines have equal slope
let this (x,y) be any point on the line
and now
the equation is
(y-y1)/(x-x1)=m
(y-9)/(x+8)=1/4
y-9=1/4x+2
y=1/4x+11

Answer 3

perpendicular line equations
we have to notice that the slope of a line perpendicular to another line is the negative reciprocal of the other.
so 1/4
would be -4
now using the slope intercept equation for one point is
(y-y1)/(x-x1)=m
puttin in
(y-9)/(x+8)=-4
y-9=-4x-32
y=-4x-23

Answer 4

those are the equations of parallel and perpendicular lines to the line y = 1/4x + 7 and that pass through the point (-8, 9).