Equation of a Line (Point-Slope) – Fast Results

Equation of a Line (Point-Slope)

This calculator helps you find the equation of a straight line when you know one point on the line and its slope. It will output the equation in the familiar slope-intercept form: y = mx + b.

Point X-coordinate (x₁)

Enter the x-value of the known point.

Point Y-coordinate (y₁)

Enter the y-value of the known point.

Slope (m)

Enter the slope of the line.

How it works

This calculator helps you find the equation of a straight line when you know one point on the line and its slope. It will output the equation in the familiar slope-intercept form: y = mx + b.

The Formula

The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a known point and m is the slope. To convert this to slope-intercept form (y = mx + b), you rearrange the equation to solve for y.

Worked Example

Example: Find the Equation
Given a point (3, 5) and a slope of 2. We use y - y₁ = m(x - x₁). So, y - 5 = 2(x - 3). Distribute the slope: y - 5 = 2x - 6. Add 5 to both sides: y = 2x - 1. Here, m = 2 and b = -1.

Tips, Assumptions & Limitations

Ensure your point coordinates (x, y) and slope (m) are entered correctly.
Remember that 'b' is the y-intercept, where the line crosses the y-axis.
A positive slope means the line rises from left to right; a negative slope means it falls.

FAQ

The point-slope form is y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a specific point on the line. It's a handy way to write a linear equation if you have these two pieces of information.

Once you have the point-slope form, simply distribute the slope 'm' on the right side, then isolate 'y' by moving the y₁ term to the right side of the equation. This will give you y = mx + b.

Yes, absolutely! This calculator is designed to work with both positive and negative values for the slope and the x and y coordinates of your point. Just enter them as usual.