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# A line passes through (2, −1) and (4, 5). Which answer is the equation of the line?

Straight lines can be represented in the form of linear equations on the cartesian plane. Let's solve a problem related to the concept of two-point form in straight lines.

## Answer: The Equation of the Line that Passes through the Points (2, −1) and (4, 5) is 3x - y - 7 = 0.

Let's solve this step by step.

**Explanation:**

We are given: (x_{1}, y_{1}) = (2, −1) and (x_{2}, y_{2}) = (4, 5)

The two-point form of a line passing through these two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is:

⇒ (y − y_{1}) = [(y_{2} − y_{1}) (x − x_{1})] / (x_{2} − x_{1})

Here, (y_{2} − y_{1}) / (x_{2} − x_{1}) is the slope of the line.

⇒ (y − y_{1}) (x_{2} − x_{1}) = (y_{2} − y_{1}) (x − x_{1})

Substituting the values of points (x_{1}, y_{1}) and (x_{2}, y_{2}):

⇒ (y - (-1)) (4 - 2) = (5 - (-1)) (x − 2)

⇒ (y + 1) (2) = (6) (x - 2)

⇒ 2y + 2 = 6x - 12

⇒ 6x - 2y - 14 = 0

⇒ 3x - y - 7 = 0

### Hence, the Equation of the Line that Passes through the Points (2, −1) and (4, 5) is 3x - y - 7 = 0.

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