What is the equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6?

Solution:

Given that the required line is parallel to 2x + 3y = 6,

Rewriting this, we get 3y = 6-2x

y = -2/3 x + 6

This is of the form y = m₁ x + C, where m₁ is the slope

The slope of the given line is -2/3

The slope of the line parallel to this line is also -2/3 [Since (m\(_1\) = m\(_2\)]

The slope of the line passing through (x\(_1\), y\(_1\)) is

y - y\(_1\) = m\(_2\) (x-x\(_1\))

Here, A = 2, B = 3 and (x\(_1\), y\(_1\)) = (-2, 3)

⇒ y - 3 =  -2/3( x + 2)

⇒ 3 (y - 3) = -2( x + 2)

⇒ 3y -9 = -2x -4

⇒ 2x + 3y - 5 = 0

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What is the equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6?

Summary :

The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.