PLEASE HURRY Which equation represents the line that passes through the point
(5, - 1) and is perpendicular to 2x – 3y = 6?

3x + 2y = 13

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

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide all terms by - 3 )

y = x - 2 ← in slope- intercept form

with slope m =

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = - , thus

y = - x + c ← is the partial equation

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

- 1 = - + c ⇒ c = - 1 + =

y = - x + ← in slope- intercept form

Multiply through by 2

2y = - 3x + 13 ( add 3x to both sides )

3x + 2y = 13 ← in standard form

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