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

Solution:

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

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.

Let the given points are (x₁, y₁) = (1, 0) and (x₂, y₂) = (3, 4).

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

We get,

⇒ y - y₁ = m (x - x₁)

⇒ m = slope formula = (y₂ - y₁) / (x₂ - x₁) 

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

You can find the slope using the slope calculator.

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

(y - 0) = m (x - 1) [Since, (y₂ - y₁) / (x₂ - x₁) = 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.

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

Summary:

The general equation of the line that passes through the given two points: (1, 0) and (3, 4) is y = 2x - 2