Answer:
d
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 = [tex]\frac{5}{2}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{5}{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{5}{2} }[/tex] = - [tex]\frac{2}{5}[/tex] , then
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation
To find c substitute (5, - 7) into the partial equation
- 7 = - 2 + c ⇒ c = - 7 + 2 = - 5
y = - [tex]\frac{2}{5}[/tex] x - 5 ← equation of perpendicular line → d
