Answer:
               
y + 3= 3(x - 6)        ←    point-slope form
               y = 3x - 21           ←    slope-intercept form
              3x - y = 21          ←    standard form
Step-by-step explanation:
The point-slope form of the equation of line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.
y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂
{Two lines are parallel if  their slopes are equal}
y = 3x + 1   ⇒    m₁ = 3    ⇒    m₂ = 3
(6, -3)    ⇒    x₁ = 6,  y₁ = -3
point-slope form:
y - (-3) = 3(x - 6)
y + 3 = 3(x - 6)
y + 3 = 3x - 18               {subtact 3 from both sides}
y = 3x - 21         ←    slope-intercept form
-3x + y = -21                 {multiply both sides by (-1)}
3x - y = 21          ←    standard form