How to Find the Equation of a Line with Two Points

To find the equation of a line given two points, you can follow these steps:

1. Identify the Points: Assume you have two points, (x₁, y₁) and (x₂, y₂).
2. Calculate the Slope: The slope (m) of the line through these two points can be calculated using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

3. Use the Point-Slope Form: With the slope calculated, you can use the point-slope form of the equation of a line:

y – y₁ = m(x – x₁)

4. Simplify to Slope-Intercept Form: If desired, you can rearrange the equation to obtain the slope-intercept form (y = mx + b) by solving for y.

For example, if your points are (1, 2) and (3, 4):

1. Calculate the slope:

m = (4 – 2) / (3 – 1) = 2 / 2 = 1

2. Use the point-slope form using point (1, 2):

y – 2 = 1(x – 1)

3. Simplify to:

y = x + 1

This is the equation of the line that passes through the two points.