Answer:
4th option
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{3}{5}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{3}{5}[/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{3}{5} }[/tex] = - [tex]\frac{5}{3}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - [tex]\frac{5}{3}[/tex] and (a, b ) = (- 2, 5 ) , then
y - 5 = - [tex]\frac{5}{3}[/tex] (x - (- 2) ) , that is
y - 5 = - [tex]\frac{5}{3}[/tex] (x + 2)