Answer:
x - 3y = 6
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 )
Given
12x + 4y = 8 ( subtract 12x from both sides )
4y = - 12x + 8 ( divide all terms by 4 )
y = - 3x + 2 ← in slope- intercept form
with slope m = - 3
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{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , thus
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, - 1) into the partial equation
- 1 = 1 + c ⇒ c = - 1 - 1 = - 2
y = [tex]\frac{1}{3}[/tex] x - 2 ← in slope- intercept form
Multiply through by 3
3y = x - 6 ( subtract 3y and add 6 to both sides )
x - 3y = 6 ← in standard form
