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

Answer:

        b)  y = -3x - 7

Step-by-step 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