Question #0443e

1 Answer
Dec 21, 2017

Answer:

#1a)   x - y = 2#
#1b) color(white)(.)x + y =# - # 2#

#2a)  x - y =# - # 3#
#2b)   x + y = 1#

Explanation:

1a) Parallel to #y = x - 3# through #(0,#-#2)#

Parallel lines have the same slope.
The point P is #b#, the #y# intercept.

So this line, parallel to the given line, is
#y = x - 2#

Standard form
#x - y = 2#
~ ~ ~ ~ ~ ~ ~

1b) Perpendicular to #y = x - 3# through #(0,#-#2)#

The point P is #b#, the #y# intercept.
The slopes of lines perpendicular to each other are the negative inverses of each other.
So the slope of the unknown line is -# 1.#

This line, perpendicular to the given line, is
#y = - x - 2#

Standard form
#x + y = - 2#
~ ~ ~ ~ ~ ~ ~ ~ ~

2a) Parallel to #y = x - 3# through (-#1,2)#

Because the lines are parallel, both slopes are 1.

To find #b#, sub in the values for #x# and #y# and solve for #b#

#y =  m    x  + b#
#2 = (1)##(#-1) #+ b#
#2 = color(white)(.)# -# 1      + b#
#3 = b#
#y = x + 3#

Standard form
#x - y =# - #3#
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

2b) Perpendicular to #y = x - 3# through (-#1,2)#
The perpendicular slope will be -#1#
The new #y# intercept will be
#y =   m (x) + b#
#2 =# *-1 (*-#1)# #+ b#
#2 = 1 + b#
#1 = b#
#y =# -#x + 1#

Standard form
#x + y = 1#