Point-Slope Form Calculator

Find the equation of a line using point-slope form. Enter a point and slope or two points to get point-slope, slope-intercept, and standard form equations with an interactive graph and step-by-step solution.

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About Point-Slope Form Calculator

The Point-Slope Form Calculator finds the equation of a line given a point and a slope, or given two points. It outputs the equation in three standard formats — point-slope form, slope-intercept form, and standard form — with a step-by-step solution and interactive coordinate plane graph.

How to Use the Point-Slope Form Calculator

Choose your input mode: Select "Point & Slope" if you know one point and the slope, or "Two Points" if you have two points on the line.
Enter the coordinates: Type the $x$ and $y$ values for your known point(s). Use the parenthesized input fields for intuitive coordinate entry.
Enter the slope (if applicable): Type the slope as a decimal (e.g., 0.5) or a fraction (e.g., 2/3). Negative slopes work too (e.g., -3/4).
Click "Calculate Equation" to see the results instantly.
Review the output: Three equation cards show the line in point-slope, slope-intercept, and standard form. Use the copy buttons to grab any equation. Scroll down for the step-by-step solution, line properties, and interactive graph.

What Is Point-Slope Form?

Point-slope form is a way of writing the equation of a straight line. If you know a point $(x_1, y_1)$ on the line and the slope $m$, the equation is:

$$y - y_1 = m(x - x_1)$$

This form is especially useful when you don't know the y-intercept directly. It's derived from the definition of slope: $m = \frac{y - y_1}{x - x_1}$.

Converting Between Forms

Point-Slope to Slope-Intercept Form

Starting from $y - y_1 = m(x - x_1)$:

Distribute: $y - y_1 = mx - mx_1$
Add $y_1$: $y = mx - mx_1 + y_1$
The result is $y = mx + b$ where $b = y_1 - mx_1$

Slope-Intercept to Standard Form

From $y = mx + b$:

Rearrange: $-mx + y = b$, or equivalently $mx - y = -b$
If $m$ is a fraction, multiply through to clear denominators
The result is $Ax + By = C$ with $A \geq 0$

Using Two Points

If you have two points $(x_1, y_1)$ and $(x_2, y_2)$, first compute the slope:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Then substitute the slope and either point into the point-slope formula. Both points give the same line.

Understanding the Graph

The interactive graph shows:

The line drawn with an animation across the coordinate plane
Your input point(s) marked with colored dots and labeled coordinates
The slope triangle (rise over run) near your point, showing the geometric meaning of slope
Intercepts: the y-intercept (green dot) and x-intercept (orange dot) where applicable

Special Cases

Horizontal line (m = 0): The equation simplifies to $y = y_1$, a constant.
Slope of 1: The line makes a 45-degree angle with the x-axis.
Negative slope: The line falls from left to right.
Fractional slope: Enter as a/b (e.g., 2/3). The calculator handles fractions natively.
Vertical lines have undefined slope and cannot be expressed in point-slope form. If your two points share the same x-coordinate, the calculator will alert you.

FAQ

What is point-slope form?

Point-slope form is a way to write the equation of a line when you know one point on the line and the slope. The formula is y - y1 = m(x - x1), where (x1, y1) is the known point and m is the slope.

How do you convert point-slope form to slope-intercept form?

Distribute the slope m across (x - x1) to get y - y1 = mx - mx1. Then add y1 to both sides: y = mx - mx1 + y1. The constant term -mx1 + y1 is the y-intercept b, giving y = mx + b.

Can you use two points instead of a point and slope?

Yes. First calculate the slope using m = (y2 - y1) / (x2 - x1), then plug the slope and either point into the point-slope formula y - y1 = m(x - x1).

What is standard form of a linear equation?

Standard form is Ax + By = C, where A, B, and C are integers and A is non-negative. It is useful for finding intercepts and for systems of equations.

What if the slope is a fraction?

You can enter fractions directly as a/b, for example 2/3 or -3/4. The calculator handles fractions and displays them properly in the results.

Reference this content, page, or tool as:

"Point-Slope Form Calculator" at https://MiniWebtool.com/point-slope-form-calculator/ from MiniWebtool, https://MiniWebtool.com/

Last updated: 2026-03-30

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