Point Slope Form

What is the Point Slope Formula?
The Point-Slope Formula is a way to find the equation of a line when you know:

• The slope \(m\) of the line.
  
• One point \((x_1, y_1)\) that the line passes through.
  

The formula is:
\(y - y_1 = m(x - x_1)\)

How to use the point-slope formula?
The following diagram shows how to use the point-slope formula to find the equation of a line. Scroll down the page for more examples and solutions.

Coordinate Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Coordinate Geometry Worksheets

1. Identify the slope \(m\): If the slope is not directly given, you might need to calculate it using two points on the line with the slope formula:
   \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
   
2. Identify one point \((x_1, y_1)\): You will be given at least one point that the line passes through.
   
3. Substitute the values into the Point-Slope Formula: Plug the values of \(m, x_1,\) and \(y_1\) into the formula:
   \(y - y_1 = m(x - x_1)\)
   Note that \(x\) and \(y\) remain as variables in the equation.
   

Point Slope Form
Learn to write the equation of a line given a point on the line and the slope of the line, by using the point-slope formula, which states that given a point (x₁, y₁) and a slope m, the equation of the line can be written as y - y₁ = m(x - x₁)

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This video covers how to find the equations of lines if you know the slope and a point using the point-slope formula.

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How to write equations of lines given the slope and a point on the line.

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Shows how to graph a line if you know the slope and one point on the line.

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