# Write an equation of the line that passes through the given two points: (1, 0) and (3, 4)

A two-point form of the equation is used when two different points on the line are known.

## Answer: The general equation of the line is y = 2x - 2

This equation can easily be simplified to any of the forms of the equation like the slope-intercept form, so as to calculate the intercept value by comparison.

**Explanation:**

Let the given points are (x_{1}, y_{1}) = (1, 0) and (x_{2}, y_{2}) = (3, 4).

Therefore, applying the slope-intercept form of the equation,

We get,

⇒ y - y_{1} = m (x - x_{1})

⇒ m = slope formula = (y_{2} - y_{1}) / (x_{2} - x_{1})

Slope of the line = m = (4 - 0) / (3 - 1) = 4 / 2 = 2

You can find thye slope using the slope calculator.

Using the point (1, 0), let's write the equation of the line.

(y - 0) = m (x - 1) [Since, (y_{2} - y_{1}) / (x_{2} - x_{1}) = m]

⇒ y = 2(x - 1)

⇒ y = 2x - 2

### Thus, the equation of the line passing through the points (1, 0) and (3, 4) is y = 2x - 2.