# What is the slope-intercept form equation of the line that passes through (1, 3) and (3, 7)?

Coordinate Geometry is a very important topic in mathematics in which various equations are represented as curves on the cartesian, polar, or other types of planes.

## Answer: The slope-intercept form equation of the line that passes through (1, 3) and (3, 7) is y = 2x + 1

Let's solve this step by step.

**Explanation:**

Now, let us have a look at the slope-intercept form of a line.

Given: (x_{1}, y_{1}) = (1, 3) and (x_{2}, y_{2}) = (3, 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) (3 − 1) = (7 − 3) (x − 1)

(y − 3) (2) = (4) (x - 1)

2y - 6 = 4x - 4

2y = 4x + 2

y = 2x + 1