Math
Point Slope Form Calculator
Enter a point and a slope, or two points, and get the line in point-slope form y - y1 = m(x - x1). mathcheck then distributes and solves to show y = mx + b, the standard and general forms, both intercepts, a graph, and each algebra step with exact fractions.
Type a fraction like 3/2 or a decimal like -0.5. Type "undefined" for a vertical line.
x-coordinate of the known point.
y-coordinate of the known point.
Try an example
Result
Point-slope form
—
- Slope-intercept form
- —
- Standard form
- —
- Slope m
- —
- Y-intercept
- —
- Point-slope form using P2
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What is point-slope form?
Point-How steep a line is: how much y changes for each step right in x. form writes a line using one known point (x1, y1) and the slope m. It comes straight from the slope formula: if m = (y - y1)/(x - x1) for every point (x, y) on the line, multiplying both sides by (x - x1) gives y - y1 = m(x - x1). It is the fastest form to write when you know a point and the slope.
From point-slope form to y = mx + b
- Distribute the slope: y - y1 = mx - m*x1.
- Add y1 to both sides: y = mx - m*x1 + y1.
- Combine the constants; the result -m*x1 + y1 is the y-A point where a graph crosses an axis. b.
Slope 3/2 through (1, 2)
y - 2 = (3/2)(x - 1) → y - 2 = (3/2)x - 3/2 → y = (3/2)x + 1/2. Standard form: multiply by 2 and rearrange to get 3x - 2y = -1.
| Form | Equation | Best when |
|---|---|---|
| Slope-intercept | y = mx + b | You want the slope and y-intercept at a glance |
| Point-slope | y - y1 = m(x - x1) | You know one point and the slope |
| Standard | Ax + By = C | Integer coefficients, intercepts, or systems of equations |
| General | Ax + By + C = 0 | Distance formulas and conic sections |
How to use this calculator
- Choose Point and slope if you know one point and m, or Two points if you know two points on the line.
- Type the slope as a fraction (3/2) or a decimal (-0.5). Type undefined for a vertical line.
- Read y - y1 = m(x - x1) in the header and the slope-intercept version in the box beneath it.
- Scroll to the grid for the intercepts and line type, and the list for the standard and general forms.
- Open Show the work to follow the distribute-and-solve steps.
How to read the answer
In y - y1 = m(x - x1), the numbers subtracted from x and y are the coordinates of the known point, and m is the slope. Watch the signs: a point with negative coordinates such as (-3, 4) gives y - 4 = m(x + 3), because subtracting -3 is adding 3. Solving for y produces the slope-intercept form, where the constant is the y-intercept.
Common mistakes and edge cases
- Sign errors with negative coordinates: (x - (-3)) is (x + 3), not (x - 3).
- Forgetting to distribute the slope to both terms inside the parentheses.
- Using the slope as a rounded decimal. Keep 2/3 as 2/3 so the y-intercept stays exact.
- A vertical line has undefined slope and cannot be written in point-slope form; it is written x = x1.
- Two identical points do not define a line, so the calculator asks for two different points.
Worked examples
Point and fraction slope
Slope 3/2 through (1, 2)
Point-slope form
y - 2 = (3/2)(x - 1)
Negative coordinates
Slope -2 through (-3, 4)
Point-slope form
y - 4 = -2(x + 3)
From two points
Line through (2, -1) and (6, 5)
Point-slope form
y + 1 = (3/2)(x - 2)
Zero slope
Slope 0 through (5, 3)
Point-slope form
y - 3 = 0(x - 5)
Decimal slope
Slope 0.25 through (0.5, -1.5)
Point-slope form
y + 3/2 = (1/4)(x - 1/2)
Vertical line
Undefined slope through (4, 1)
Point-slope form
x = 4
Bad slope text
Slope typed as "three halves"
Point-slope form
—
Frequently asked questions
What is the point-slope formula?+
y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line. It is the slope formula rearranged so that (x, y) can be any point on the line.
How do I convert point-slope form to slope-intercept form?+
Distribute m across (x - x1), then add y1 to both sides. For y - 2 = 3(x - 1): y - 2 = 3x - 3, so y = 3x - 1.
Which point do I use if I have two points?+
Either one. y - y1 = m(x - x1) and y - y2 = m(x - x2) both simplify to the same slope-intercept equation. The calculator shows both versions so you can match your textbook.
Why does the sign flip for negative coordinates?+
Point-slope form subtracts the coordinates. Subtracting a negative number is the same as adding, so the point (-3, 4) gives y - 4 = m(x + 3).
Can I write a vertical line in point-slope form?+
No. A vertical line has an undefined slope, so there is no m to multiply by. Write it as x = x1 instead.
How do I get standard form from point-slope form?+
Solve for y first, then move the x-term to the left side and multiply by the denominator so A, B, and C are integers. The calculator shows the reduced standard form automatically.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Slope Calculator
Find slope from two points, solve a missing coordinate from a known slope, or turn an angle or percentage grade into a slope. Includes equations, intercepts, perpendicular slope, graph, and step-by-step work.
Slope Intercept Form Calculator
Write the equation of a line in slope-intercept form y = mx + b from two points, a point and a slope, or standard form. Exact fractions, intercepts, a graph, and every other form of the line.
Standard Form to Slope Intercept Form Calculator
Convert a line between standard form Ax + By = C and slope-intercept form y = mx + b in either direction, with integer-cleared coefficients, exact fractions, intercepts, and steps.
Parallel Line Calculator
Find the equation of the line parallel to a given line through a point. Accepts y = mx + b, two points, point-slope, or standard form, and graphs both lines with the distance between them.
Perpendicular Line Calculator
Find the equation of the line perpendicular to a given line through a point using the negative reciprocal slope. Accepts any line form, graphs both lines, and shows where they meet at a right angle.
X and Y Intercepts Calculator
Find the x-intercept and y-intercept of a line given in any form, or the intercepts of a quadratic y = ax^2 + bx + c, with exact fractions, radicals, and the substitution steps.
Last updated: September 4, 2026