Enter a point and a slope, or two points, to get the equation of the line in point-slope form y − y₁ = m(x − x₁). The calculator also converts it to slope-intercept form (y = mx + b) and standard form (Ax + By = C), finds both intercepts and graphs the line.
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Fractions like 3/4 keep the answer exact.
Enter your values to see the result.
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How to use the Point Slope Form Calculator
Choose what you know: one point and the slope, or two points on the line.
Enter the coordinates (and the slope). Whole numbers, decimals and fractions like −2/3 all work.
Press Calculate. The point-slope form appears at the top.
Read the other forms: slope-intercept, standard form and the intercepts.
Check the steps and graph to see how the equation was built.
Point-slope with the first point: y − 4 = −3/4 (x + 3).
Distribute: y − 4 = −(3/4)x − 9/4, so y = −(3/4)x + 7/4.
Standard form: multiply by 4 and rearrange: 3x + 4y = 7.
Check with the second point: 3(5) + 4(−2) = 15 − 8 = 7 ✓
Common mistakes
Sign errors: the form has minus signs built in, so a point with negative coordinates produces plus signs: (−2, −1) gives y + 1 = m(x + 2).
Swapping coordinates: x₁ goes with x and y₁ with y. Writing y − x₁ is a frequent slip.
Mixing the order in the slope formula: if you subtract point 2 minus point 1 on top, do the same on the bottom.
Special lines: a horizontal line has slope 0 (y = constant); a vertical line has an undefined slope (x = constant).
Frequently asked questions
What is point-slope form?
Point-slope form is y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is any point on the line. It is the quickest way to write a line's equation when you know one point and the slope: just substitute the three numbers.
How do I write point-slope form from two points?
First find the slope: m = (y₂ − y₁) ÷ (x₂ − x₁). Then substitute it with either point. For (1, 2) and (4, 11): m = 9 ÷ 3 = 3, so y − 2 = 3(x − 1). Using the other point, y − 11 = 3(x − 4) describes the same line.
How do I handle negative coordinates?
Subtracting a negative turns into addition. For the point (−2, 5) and slope 3/4: y − 5 = 3/4(x − (−2)), which simplifies to y − 5 = (3/4)(x + 2).
How do I convert point-slope form to slope-intercept form?
Distribute the slope and solve for y. From y − 5 = (3/4)(x + 2): y − 5 = (3/4)x + 3/2, so y = (3/4)x + 13/2. The constant b = y₁ − m·x₁ is the y-intercept.
How do I convert to standard form?
Move the x term to the left side and multiply through by the least common denominator so A, B and C are integers, with A not negative. y = (3/4)x + 13/2 becomes 3x − 4y = −26.
What about vertical lines?
If both points have the same x value, the slope is undefined (division by zero), so the line has no point-slope or slope-intercept form. Its equation is simply x = a, for example x = 3.
Is the point-slope form unique?
No. Every point on the line gives a different-looking point-slope equation, but they all simplify to the same slope-intercept form. That is why teachers often ask for the slope-intercept or standard form as the final answer.
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