Put in Point Slope Form Calculator

The point-slope form of a linear equation is a way to express the equation of a straight line using a point on the line and the slope of the line. This form is particularly useful when you know the slope of the line and a point through which the line passes.

What is Point-Slope Form?

The point-slope form of a linear equation is written as:

y - y₁ = m(x - x₁)

Where:

m is the slope of the line
(x₁, y₁) is a point on the line

This form is useful because it directly incorporates the slope and a specific point on the line, making it easy to write the equation of a line when this information is known.

How to Convert to Point-Slope Form

To convert a linear equation to point-slope form, follow these steps:

Identify the slope (m) of the line.
Identify a point (x₁, y₁) that lies on the line.
Substitute the values of m, x₁, and y₁ into the point-slope form equation: y - y₁ = m(x - x₁).

For example, if you have the equation y = 2x + 3 and you know the line passes through the point (1, 5), you can write it in point-slope form as:

y - 5 = 2(x - 1)

Examples

Example 1

Given the equation y = -3x + 7 and the point (2, 1), convert to point-slope form.

y - 1 = -3(x - 2)

Example 2

Given the equation y = (1/2)x - 4 and the point (4, -6), convert to point-slope form.

y - (-6) = (1/2)(x - 4)

y + 6 = (1/2)(x - 4)

FAQ

What is the point-slope form used for?: The point-slope form is used to write the equation of a line when you know the slope of the line and a point through which the line passes. It's particularly useful in geometry and algebra.
How do I find the slope of a line?: The slope (m) of a line can be found using the formula m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
Can I convert point-slope form to slope-intercept form?: Yes, you can convert point-slope form to slope-intercept form (y = mx + b) by solving for y. For example, y - y₁ = m(x - x₁) can be rewritten as y = mx - mx₁ + y₁, which is y = mx + (y₁ - mx₁).