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

We will be using the concept of the Point-Slope Form of a line to solve this.

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

Let's solve this step by step.

**Explanation:**

Given: (x_{1}, y_{1}) = (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 − y_{1}) = m (x − x_{1})

Substituting the values of m = 3/2 and (x_{1}, y_{1}) = (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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