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
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.
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