Write the equation of a line in point-slope form given a point and a slope, with conversion to other forms.
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Point (x₁, y₁)
Result
Equation in point-slope form.
Slope-intercept form
y = 2x + 1
Standard form
2x - y = -1
Also in Functions
Algebra
The point-slope form calculator writes the equation of a line given a single point and a slope. It produces the equation in point-slope form and converts it to slope-intercept and standard forms.
Point-slope form is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line. This form is derived directly from the definition of slope and is the most natural way to write a line when you already know one point and the steepness.
To convert to slope-intercept form, distribute m and isolate y. For example, y - 2 = 3(x - 1) becomes y = 3x - 1.
y - y1 = m(x - x1)
Point-slope form of a line through (x1, y1) with slope m.
Point-slope form is especially useful when you know the slope from context (a rate of change, a derivative) and one data point. It avoids the extra step of computing the y-intercept before writing the equation.
Frequently asked questions
No. Any point on the line can be used as (x1, y1), so the same line can be written in different point-slope forms. They all simplify to the same slope-intercept equation.
No. Vertical lines have an undefined slope, so point-slope form does not apply. Vertical lines are written as x = a constant.
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