Answer:
C
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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-6}{4-0}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c
the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - [tex]\frac{3}{2}[/tex] x + 6 ← equation in slope- intercept form
multiply through by 2 to clear the fraction
2y = - 3x + 12 ( add 3x to both sides )
3x + 2y = 12 ← equation in standard form
