Answer:
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{9}{2}[/tex]
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 = - 4x + 38 is in this form with slope m = - 4
The line ST is perpendicular to line RS ( angles in a square are 90° )
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}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute (2, - 4) into the partial equation
- 4 = [tex]\frac{1}{2}[/tex] + c ⇒ c = - 4 - [tex]\frac{1}{2}[/tex] = - [tex]\frac{9}{2}[/tex]
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{9}{2}[/tex] ← equation of ST
