Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 4 ← is in slope- intercept form
with slope m = 1
Parallel lines have equal slopes, thus
y = x + c ← is the partial equation
To find c substitute (- 1, 1) into the partial equation
1 = - 1 + c ⇒ c = 1 + 1 = 2
y = x + 2 ← equation of parallel line
The slope of a perpendicular line is the negative reciprocal, thus
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1
y = - x + c ← is the partial equation
To find c substitute (- 1, 1) into the partial equation
1 = 1 + c ⇒ c = 1 - 1 = 0
y = - x ← equation of perpendicular line
