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Sagot :
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{19}{3}[/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 = 3x + 6 ← 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] , thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c , substitute (4, 5) into the partial equation
5 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = 5 + [tex]\frac{4}{3}[/tex] = [tex]\frac{19}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{19}{3}[/tex] ← equation of perpendicular line
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