Consider the line
y = 5/6 x + 4

find the equation of the line that is parallel to this line and passes through the point
−6,5

find the equation of the line that is perpendicular to this line and passes through the point
−6, 5

Y - y₁ = m(x - x₁)
y - 5 = ⁵/₆[x - (-6)]
y - 5 = ⁵/₆(x + 6)
y - 5 = ⁵/₆(x) + ⁵/₆(6)
y - 5 = ⁵/₆x + 5
  + 5          + 5
     y = ⁵/₆x + 10

y - y₁ = m(x - x₁)
y - 5 = -1¹/₅[x - (-6)]
y - 5 = 1¹/₅(x + 6)
y - 5 = 1¹/₅(x) + 1¹/₅(6)
y - 5 = 1¹/₅x + 7¹/₅
  + 5           + 5
     y = 1¹/₅x + 12¹/₅