# Write the Equation of the Line that Passes through (−2, 6) and (2, 14) in Slope-Intercept Form.

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

## Answer: The Equation of the Line that Passes through (−2, 6) and (2, 14) in Slope-Intercept Form is y = 2x + 10

Let's solve this step by step.

**Explanation:**

Given that, (x\(_1\), y\(_1\)) = (−2, 6) and (x\(_2\), y\(_2\)) = (2, 14)

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 − 6) (2 − {-2}) = (14 − 6) (x − {-2})

(y − 6) (4) = (8) (x + 2)

4y - 24 = 8x + 16

4y = 8x + 40

y = 2x + 10