How do you find the equation of a line given two points?

Finding the Equation of a Line from Two Points

To find the equation of a line from two points, use the point-slope form:
y - y1 = m(x - x1)

Steps:

• 1. Find the slope (m):

For points (x₁, y₁) and (x₂, y₂),
 m = (y₂ - y₁) / (x₂ - x₁)

• 2. Plug in one point:

Use either point as (x₁, y₁) and your calculated m.

• 3. Simplify (optional):

You can rearrange to slope-intercept form: y = mx + b.

Example:
Given points (2, 3) and (4, 7):

• Find the slope:

 m = (7 - 3) / (4 - 2) = 4 / 2 = 2

• Use point-slope form with (2, 3):

 y - 3 = 2(x - 2)

• Simplify:

 y - 3 = 2x - 4
 y = 2x - 1

Takeaways:

• Find slope with m = (y₂ - y₁)/(x₂ - x₁) and plug into point-slope form.
• Final equation can be left in point-slope or converted to slope-intercept form.