Hurry and answer please

Question

Which equation represents the line passing through the points (3, 2) and (–9, 6)?

[A] x – 3y = 9

[B] x + 3y = 9

[C] 3x – y = -9

[D] 3x + y = 9

Explain your thinking.

Answer 1

First, we must calculate the slope using the formula, m = (y₂ - y₁) / (x₂ - x₁).

Let x₁, y₁ = (3, 2) and x₂, y₂ = (-9, 6)

m = (6 - 2) / (-9 - 3) = 4 / -12. This can be reduced to -1/3.

Now, we plug in the point x₁, y₁ = (3, 2) and slope m = -1/3 into the point slope formula: y - y₁ = m (x - x₁).

y - 2 = (-1/3)(x - 3)

Distribute the slope to (x-3):

y - 2 = (-1/3)(x) + 1

Add two to both sides:

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

The equation must be in standard form (Ax + By = C, where A, B, and C are NOT fractions) so let's add (1/3)x to the other side:

(1/3)x + y = 3

Multiply both sides of the equation by 3 to get rid of the fraction:

x + 3y = 9

Answer 2

If points are on a line then the coordinates of each point must solve the equation. For which equation does the two pairs of coordinates solve?