Question

Which is an equation of the line through (-1, -4) and parallel to 3x+y=5

a) y= 3x + 1
b) y= -3x - 7
c) y= -3x + 7
d) y= 3x - 1

Answer 1

b) y = -3x - 7

Explanation:

3x + y = 5 {subtract 3x from both sides}

y = -3x + 5 ← slope-intercept form

y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂

{Two lines are parallel if their slopes are equal}

y = -3x + 5 ⇒ m₁ = -3 ⇒ m₂ = -3

(-1, -4) ⇒ x₁ = -1, y₁ = -4

The point-slope form:

y - (-4) = -3(x - (-1))

y + 4 = -3(x + 1)

y + 4 = -3x - 3 {subtact 4 from both sides}

y = -3x - 7 ← slope-intercept form