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 )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with ( x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 0)
m = [tex]\frac{0+3}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{4}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (4, - 6) into the partial equation
- 6 = - [tex]\frac{16}{3}[/tex] + c ⇒ c = - 6 + [tex]\frac{16}{3}[/tex] = - [tex]\frac{2}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← in slope- intercept form
Multiply all terms by 3
3y = - 4x - 2 ( add 4x to both sides )
4x + 3y = - 2 ← in standard form
