Find the equation for the line that passes through the point (1,-5) and that is perpendicular to the line with the equation y=1/3x-2/3

Respuesta :

Answer:

y = - 3x - 2

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{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/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{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute (1, - 5 ) into the partial equation

- 5 = - 3 + c ⇒ c = - 5 + 3 = - 2

y = - 3x - 2 ← equation of perpendicular line

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