Given one point on a line and its slope, this writes the line’s equation in point-slope form and converts it to slope-intercept form as well.
How it works
The point and slope are substituted directly into y − y1 = m(x − x1), then rearranged into y = mx + b for the slope-intercept version.
What this does not include
This does not include finding the slope from two points — for that, use this site’s slope-intercept form calculator instead, which takes two points directly.
How to use this calculator
- Enter a point (x1, y1) on the line and its slope.
A worked example
Point (2, 3), slope 4: point-slope form is y − 3 = 4(x − 2), converting to slope-intercept form y = 4x − 5.
Point (−1, 5), slope −2: slope-intercept form is y = −2x + 3.
What the variables mean
| Variable | Meaning |
|---|---|
| (x1, y1) | A known point on the line |
| Slope | The line’s slope |
Edge cases worth knowing
Point-slope form needs only one point and the slope — unlike the two-point slope-intercept calculator, which needs two full points to derive the slope first.
A missing x-coordinate makes the equation impossible to write — without a specific point, there’s no line to describe, so the calculator declines to show a result.
Frequently asked questions
What’s the difference between point-slope and slope-intercept form?
Point-slope form is built directly from one point and the slope; slope-intercept form rearranges that same line into the y = mx + b shape, which is more useful for graphing.
Why is point-slope form useful?
It’s often the fastest way to write a line’s equation when you already know a single point and the slope, without needing to solve for the y-intercept separately.
Does the choice of point matter?
No — any point on the same line with the same slope produces an equation that simplifies to the identical slope-intercept form.
