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Two-point form
(y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁)
Where: x = Two-point form, x₁ = x₁, x₂ = x₂, y = y, y₁ = y₁, y₂ = y₂
Solved example
Given: x_1 = 7, x_2 = 5, y = 10, y_1 = 4, y_2 = 3
Find: x (Two-point form)
- Formula: (y - y₁)/(-y₁ + y₂) = (x - x₁)/(-x₁ + x₂)
- Rearranged for x: x = (x₁·y - x₁·y₂ - x₂·y + x₂·y₁)/(y₁ - y₂)
- Substitute the values: x = (-10·5 + 10·7 - 3·7 + 4·5)/(-3 + 4)
- Result: x = 19
Answer: x = 19
Calculator
How to calculate Two-point form
- Write down the formula: (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁).
- Note the known values (x₁, x₂, y, y₁, y₂).
- Substitute them and simplify to find x.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Two-point form?
The formula is (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁), where x = Two-point form, x₁ = x₁, x₂ = x₂, y = y, y₁ = y₁, y₂ = y₂.
What is Two-point form when x_1 = 7, x_2 = 5, y = 10, y_1 = 4, y_2 = 3?
x = 19. Substitute the values into (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁) and simplify.