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Find the equation of the line that passes through (-1,2)and is perpendicular to 2y=x-3

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Answer:

y = - 2x

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 )

Given

2y = x - 3 ( divide the terms by 2 )

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

with slope m = [tex]\frac{1}{2}[/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}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

To find c, substitute (- 1, 2) into the partial equation

2 = 2 + c ⇒ c = 2 - 2 = 0

y = - 2x ← equation of the perpendicular line

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