Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (3, 2)
m = [tex]\frac{2-1}{3+3}[/tex] = [tex]\frac{1}{6}[/tex], thus
y = [tex]\frac{1}{6}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 2), then
2 = [tex]\frac{1}{2}[/tex] + c ⇒ c = [tex]\frac{3}{2}[/tex], thus
y = [tex]\frac{1}{6}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
Multiply through by 6
6y = x + 9 ( subtract 6y from both sides )
0 = x - 6y + 9 ( subtract 9 from both sides )
- 9 = x - 6y, that is
x - 6y = - 9 ← in standard form → B
