Point-Slope Form Calculator
Turn a single point and a slope into both the point-slope and slope-intercept equations of a line.
y − y₁ = m(x − x₁)
y = mx + b, with b = -5
Step by step
- Start: y − y₁ = m(x − x₁)
- b = y₁ − m·x₁ = 3 − (4)(2) = -5
- So y = 4x − 5
How it works
Point-slope form is the quickest way to write a line's equation when you know one point on it and its slope. The template is y − y₁ = m(x − x₁): just drop in the slope for m and the point's coordinates for x₁ and y₁.
From there, slope-intercept form (y = mx + b) is a short hop away. Distribute the slope and solve for y, which gives b = y₁ − m·x₁, the y-intercept. Both equations describe the exact same line — they're just written differently.
This calculator writes out both forms and shows how it finds b. Negative coordinates are handled cleanly, so a point like (−2, 3) turns into y − 3 = m(x + 2) without any sign confusion.
Frequently asked questions
When should I use point-slope form?
It shines when you're handed a point and a slope, or a point and enough info to find the slope. You can plug the values straight in without solving for the y-intercept first, which saves a step.
How is point-slope related to slope-intercept form?
They're the same line in different clothes. Start with y − y₁ = m(x − x₁), distribute the m, and move y₁ across, and you land on y = mx + b where b = y₁ − m·x₁.
What if my slope is zero?
A slope of 0 means a horizontal line. The point-slope form becomes y − y₁ = 0, which simplifies to y = y₁ — a constant. The tool shows this as y equal to your point's y-value.