What is the Equation of the Line that Passes through the Points (1, 1) and (5, 5)?

Solution:

We will be using the concept of the Point-Slope Form of a line to solve this. 

Given that, (x₁, y₁) = (1, 1) and (x₂, y₂) = (5, 5)

We need to find the slope first.

Slope Formula (m) = (y₂ - y₁) / (x₂ - x₁)

On substituting the values, we get

Slope(m) = (5 - 1) / (5 - 1)

Slope(m) = 4/4

Slope(m) = 1

You can also calculate the slope using Cuemath's slope calculator.

The point-slope formula states (y - y₁) = m (x - x₁).

Substituting the values, we get (y - 1) = 1 × (x - 1) 

⇒ y - 1 = x - 1

x - y = 0

Hence, the equation of the line passing through the given points (1, 1), (5, 5) is x - y = 0.

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What is the Equation of the Line that Passes through the Points (1, 1) and (5, 5)?

Summary:

The Equation of the Line Passing through the given Points (1, 1) and (5, 5) is x - y = 0.