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