📈 点斜式方程计算器Point-Slope Form Calculator
由两点或一点加斜率求直线的点斜式方程 y − y₁ = m(x − x₁)，并同时给出斜截式和一般式（标准式），斜率尽量以分数显示。Get the point-slope equation y − y₁ = m(x − x₁) of a line from two points or a point and the slope, with the slope-intercept and standard forms too; slopes are shown as fractions where possible.
使用说明与常见问题How-to & FAQ
「点斜式方程计算器」是什么？What is the Point-Slope Form Calculator tool?
由两点或一点加斜率求直线的点斜式方程 y − y₁ = m(x − x₁)，并同时给出斜截式和一般式（标准式），斜率尽量以分数显示。Get the point-slope equation y − y₁ = m(x − x₁) of a line from two points or a point and the slope, with the slope-intercept and standard forms too; slopes are shown as fractions where possible.
如何使用「点斜式方程计算器」？How do I use the Point-Slope Form Calculator tool?
在「点斜式方程计算器」中，填写「已知」、「x₁」、「y₁」、「x₂」、「y₂」等参数，结果会随输入实时计算并显示在下方。In the Point-Slope Form Calculator: Fill in "Given", "x₁", "y₁", "x₂", "y₂"; results are recalculated instantly as you type.
点斜式是什么？What is point-slope form?
过点 (x₁, y₁)、斜率为 m 的直线可写成 y − y₁ = m(x − x₁)。已知一个点和斜率时最直接。A line through (x₁, y₁) with slope m is y − y₁ = m(x − x₁) — the most direct form when you know a point and the slope.
两点怎么求斜率？How is the slope found from two points?
m = (y₂ − y₁) ÷ (x₂ − x₁)。若 x₁ = x₂，直线竖直，斜率不存在，方程为 x = x₁。m = (y₂ − y₁) ÷ (x₂ − x₁). If x₁ = x₂ the line is vertical, has no slope, and its equation is x = x₁.
一般式什么时候是整数系数？When does the standard form have integer coefficients?
斜率和截距都能化为分母不超过 10000 的分数时，一般式 Ax + By = C 用互质整数且 A ≥ 0。输入的小数如 0.3333333333 不严格等于 1/3，会保留小数系数，并提示接近的分数；想要整数系数可改用两点模式。When the slope and intercept are fractions with denominators up to 10,000, Ax + By = C uses coprime integers with A ≥ 0. A typed decimal such as 0.3333333333 is not exactly 1/3, so decimals are kept and the nearby fraction is noted; use two-point mode for integer coefficients.
计算精度如何？How precise are the results?
「点斜式方程计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Point-Slope Form Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「点斜式方程计算器」免费吗？需要注册吗？Is the Point-Slope Form Calculator free? Do I need an account?
「点斜式方程计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Point-Slope Form Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.