Answer:
y = - 2x + 4
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 2x - 4y + 3 = 0 into this form
Subtract 2x + 3 from both sides
- 4y = - 2x - 3 ( divide all terms by - 4 )
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/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{1}{\frac{1}{2} }[/tex] = - 2, thus
y = - 2x + c ← is the partial equation
To find c substitute (5, - 6) into the partial equation
- 6 = - 10 + c ⇒ c = - 6 + 10 = 4
y = - 2x + 4 ← equation of perpendicular line
