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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