Question

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

Answer 1

Answer:

$y = \frac{-x}{3} + 5$

Step-by-step 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 = $\frac{y_{2} -y_{1}}{x_{2} -x_{1}} =\frac{6 - 7}{-3 + 6} =\frac{-1}{3}$

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,

$(y - 7) = \frac{-1}{3}(x - (-6))$

$(y - 7) = \frac{-1}{3}(x + 6)$

$3y - 21 = -x - 6$

$3y = -x - 6 + 21$

$3y = -x + 15$

$y = \frac{-x + 15}{3}$

$y = \frac{-x}{3} + 5$

Option B is the correct answer.

Answer 2

Answer:

b

Step-by-step explanation: