What is the equation of a line passing through (-6, 5) and having a slope of 1/3?

Question

A: y = 1/3x - 23/3

B: y = 1/3x - 3

C: y += 1/3x + 7

D: y = 3x+7

Answer 1

Using point-slope form:

 

1/3 = (y - 5) / (x - (-6))

1/3 = (y - 5) / (x + 6)

(x + 6) / 3 = (y - 5)

x + 6 = 3(y - 5)

x + 6 = 3y - 15

x + 21 = 3y

x/3 + 7 = y

 

D.

Answer 2

The equation of a line in point-slope form is:    (y-y₁)=m(x-x₁)     where m=slope

Using (x₁,y₁) is (-6,5):

   (y-5)= (1/3)(x-(-6))

   (y-5) = (1/3)(x+6)

    y-5 = (1/3)x + 2           [distribute]

    y = (1/3)x + 7              [add 5 to both sides]

 

Check:

  Does the line y=(1/3)x + 7 contain the point (-6,5)?

   Is  5 = (1/3)(-6) + 7   ?

        5 =  (-2) + 7?

        5 = 5   ?yes