Equation of a Line: Two Point Form

Summary

This math recipe will help you find the equation of a line, that passes through two given points.

Skill Level

Easy

Time

Approx. 1 min

Ingredients

The points through which the line passes: (x­₁, y­­₁) and (x₂, y­­₂)

Method

To find the equation of the line, we’ll use the following:

(y – y₁) = {(y₂ – y₁)/(x₂ – x₁)}(x – x₁)

Examples

Example 1 Find the equation of a line that passes through (4, 2) and (5, -1).

Solution To find the equation, we’ll use the above form directly.

y – 2 = {(5 – 4)/(2 – (-1))}(x – 4)

⇒ y – 2 = 3(x – 4)

⇒ 3x + y – 14 = 0

The figure shows the line on the XY plane.

Example 2 Find the equation of a line that passes through (1, -3) and (-2, -3).

Solution To find the equation, we’ll use the above form directly.

(y – (-3)) = {(-3 – (-3))/(2 – 1)}(x – 1)

⇒ y + 3 = 0(x – 1)

⇒ y + 3 = 0

The figure shows the line on the XY plane.

Example 3 Find the equation of a line that passes through (-2, 3) and (0, 5).

Solution To find the equation, we’ll use the above form again.

(y – 3) = {(5 – 3)/(0 – (-2))}(x – (-2))

⇒ (y – 3) = 1(x + 2)

⇒ x – y + 5 = 0

The figure shows the line on the XY plane.

That’s it for this recipe. Hope you found it helpful.

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