What is the Equation of the Line that Passes through (4, 2) and is Parallel to 3x - 2y = -6?

Solution:

Given: (x₁, y₁) = (4, 2) and Parallel to 3x - 2y = -6

Let's calculate the slope of 3x - 2y = -6 

Rewrite the equation in y = mx + c form

3x - 2y = -6

⇒ 2y = 3x + 6

⇒ y = 3/2 x + 3

Thus, Slope(m) = 3/2

As the line is parallel to 3x - 2y = -6, it will also have a slope of 3/2.

The point-slope formula states (y - y₁) = m (x - x₁)

Substituting the values of m = 3/2 and (x₁, y₁) = (4, 2) in the above equation we get,

⇒ (y - 2) = (3/2) (x - 4)

⇒ 2y - 4 = 3x - 12

⇒ 3x – 2y = 8

Hence, The equation of the line that passes through (4, 2) and is parallel to 3x - 2y = -6 is 3x - 2y = 8.

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What is the Equation of the Line that Passes through (4, 2) and is Parallel to 3x - 2y = -6?

Summary:

The Equation of the Line that Passes through (4, 2) and is Parallel to 3x - 2y = -6 is 3x - 2y = 8.