Answer:
x - 2y = - 3
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 2x + y = 3 ( subtract 2x from both sides )
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] = [tex]\frac{1}{2}[/tex] , thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (5, 4) into the partial equation
4 = [tex]\frac{5}{2}[/tex] + c ⇒ c = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
Multiply through by 2
2y = x + 3 ( subtract 2y from both sides )
0 = x - 2y + 3 ( subtract 3 from both sides )
- 3 = x - 2y , that is
x - 2y = - 3 ← in standard form
