# Question 0443e

Dec 21, 2017

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
$2 = \left(1\right)$(-1) $+ b$
$2 = \textcolor{w h i t e}{.}$ - 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
$x + y = 1$