Answer:
(a) y = 2x - 10 , (b) y =
x +

Explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given y = 3 + 2x = 2x + 3 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes , then
y = 2x + c ← is the partial equation
to find c substitute (3, - 4 ) into the partial equation
- 4 = 2(3) + c = 6 + c ( subtract 6 from both sides )
- 10 = c
y = 2x - 10 ← equation of parallel line
(b)
given
6x + 2y + 43 = 0 ( subtract 6x + 43 from both sides )
2y = - 6x - 43 ( divide through by 2 )
y = - 3x - 21.5 ← in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
= -
= -
=
, then
y =
x + c ← is the partial equation
to find c substitute (1, 5 ) into the partial equation
5 =
(1) + c =
+ c ( subtract
from both sides )
-
= c , so c =

y =
x +
← equation of perpendicular line