Answer:
y = - [tex]\frac{1}{2}[/tex] x
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 )
Rearrange 8x - 4y = 12 into this form
Subtract 4x from both sides
- 4y = - 8x + 12 ( divide all terms by - 4 )
y = 2x - 3 ← in slope- intercept form
with slope m = 2
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}{2}[/tex]
Since the line passes through the origin then c = 0
y = - [tex]\frac{1}{2}[/tex] x ← equation of perpendicular line
