Answer:
x + 2y - 8 = 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 )
y = 2x - 7 ← is 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], thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = - 1 + c ⇒ c = 3 + 1 = 4
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation in slope- intercept form
The equation of a line in general form is
Ax + By + C = 0 ( A is a positive integer and B, C are integers )
Multiply the slope- intercept equation through by 2
2y = - x + 8 ( add x to both sides )
x + 2y = 8 ( subtract 8 from both sides )
x + 2y - 8 = 0 ← in general form
