Answer:
see explanation
Step-by-step explanation:
1
(a)
Calculate slope m using the slope formula
m = 
with (x₁, y₁  = (8, 3) and (x₂, y₂ ) = (10, 7)
m =  =
 =  = 2
 = 2
(b)
Given a line with slope m then the slope of a line perpendicular to it is
 = -
 = -  = -
 = - 
(c)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = -  , then
 , then
y = -  x + c ← is the partial equation
 x + c ← is the partial equation
To find c substitute (8, 3) into the partial equation
3 = - 4 + c ⇒ c = 3 + 4 = 7
y = -  x + 7 ← equation of perpendicular line
 x + 7 ← equation of perpendicular line
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2
(a)
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (4, 4)
m =  =
 =  = - 1
 = - 1
(b)
 = -
 = -  = 1
 = 1
(c)
y = x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = 3 + c ⇒ c = 5 - 3 = 2
y = x + 2 ← equation of perpendicular line