Write the equation of a line in point-slope form given a point and a slope, with conversion to other forms.
Last updated
Point (x₁, y₁)
Result
Equation in point-slope form.
Slope-intercept form
y = 2x + 1
Standard form
2x - y = -1
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.
A worked example helps translate the point-slope form of a linear equation maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
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.
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
Also in Functions
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