# What is the Equation of the Line that Passes through the Points (−2, 3) and (2, 7)?

We will be using the two-point form of a line to solve this.

## Answer: The Equation of the Line that Passes through the Two Points (−2, 3) and (2, 7) is y = x + 5

Let's solve this step by step.

**Explanation:**

Given that, (x_{1}, y_{1}) = (-2, 3) and (x_{2}, y_{2}) = (2, 7)

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})

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

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

(y − 3) (2 − {-2}) = (7 − 3) (x − {-2})

(y − 3) (4) = (4) (x + 2)

4y - 12 = 4x + 8

4y = 4x + 20

y = x + 5