Question

Which equation represents the line that passes through (–6, 7) and (–3, 6)?

y = –y equals negative StartFraction one-third EndFraction x plus 9.x + 9
y = –y equals negative StartFraction one-third EndFraction x plus 5.x + 5
y = –3x – 11y
y = –3x + 25

Answer 1

b

Explanation:

Answer 2

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

Explanation:

Given A (x₁, y₁) = ( -6, 7) and B (x₂, y₂) = (-3, 6)

Slope of line passing through points ( -6, 7) and (-3, 6) is:

m =
`(y_(2) -y_(1))/(x_(2) -x_(1)) =(6 - 7)/(-3 + 6) =(-1)/(3)`

Now, the equation of line in point-slope form:

(y - y₁) = m (x - x₁)

Substituting the value of m and (x₁, y₁) = ( -6, 7) in above equation,

`(y - 7) = (-1)/(3)(x - (-6))`

`(y - 7) = (-1)/(3)(x + 6)`

`3y - 21 = -x - 6`

`3y = -x - 6 + 21`

`3y = -x + 15`

`y = (-x + 15)/(3)`

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

Option B is the correct answer.