Point-Slope Form

Point-Slope Form

Point-slope form is a way to write the equation of a line when you know one point on the line and the slope. It is written as

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

How to write the equation

1. Identify the point (x₁, y₁) and the slope m.
2. Substitute them into the formula exactly.
3. Be careful with signs. If the point has a negative coordinate, keep the subtraction notation unchanged.
4. Simplify the final answer if the exercise asks you to. That may mean removing parentheses and rewriting the equation in a cleaner form.

Example structure

If the point is (2, -3) and the slope is 4, write:

y - (-3) = 4(x - 2)

Then simplify to:

y + 3 = 4(x - 2)

Check your work

Make sure the point satisfies the equation. Substitute x = x₁ and y = y₁; both sides should match. Also confirm the slope changes y by m for each 1-unit change in x.