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{7}{5}[/tex] x - 3 ← is in slope- intercept form
with slope m = [tex]\frac{7}{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{7}{5} }[/tex] = - [tex]\frac{5}{7}[/tex] , then
y = - [tex]\frac{5}{7}[/tex] x + c ← is the partial equation
To find c substitute (- 4, 4 ) into the partial equation
4 = [tex]\frac{20}{7}[/tex] + c ⇒ c = 4 - [tex]\frac{20}{7}[/tex] = [tex]\frac{28}{7}[/tex] - [tex]\frac{20}{7}[/tex] = [tex]\frac{8}{7}[/tex]
y = - [tex]\frac{5}{7}[/tex] x + [tex]\frac{8}{7}[/tex] ← equation of perpendicular line
