Answer:
see explanation
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 = 3x - 4 ← is in slope- intercept form
with slope m = 3
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}{3}[/tex], hence
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the line
To find c substitute (2, 1 ) into the partial equation
1 = - [tex]\frac{2}{3}[/tex] + c ⇒ c = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
