Answer:
A
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 ) = (4, - 1) and (x₂, y₂ ) = (- 2, 3)
m = [tex]\frac{3+1}{-2-4}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex] , thus
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3) , then
3 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{4}{3}[/tex] = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
Multiply through by 3 to clear the fractions
3y = - 2x + 5 ( add 2x to both sides )
2x + 3y = 5 ( subtract 5 from both sides )
2x + 3y - 5 = 0 ← in general form
