Linear Equations
8-5Determining an Equation of a Line
Overview
Use point-slope form y − y₁ = m(x − x₁) or fit y = mx + b with the slope and a point.
Key ideas
- Need the slope and at least one point.
- With two points: find slope first.
- Solve for b by substituting a known point.
Worked examples
Example 1
Problem. Equation of a line with slope 2 through (1, 5).
Solution. y − 5 = 2(x − 1) → y = 2x + 3.
Example 2
Problem. Through (2, 4) and (4, 10).
Solution. m = 3; y − 4 = 3(x − 2) → y = 3x − 2.
Practice
Try each one. Click Show answer when ready.
- 1.
Slope 4, through (0, −1).
- 2.
Through (1, 2) and (3, 8).
- 3.
Slope −2, through (3, 1).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Find the equation of the line with slope −2 passing through (3, 1).
- 2.
Find the equation of the line through (2, 5) and (4, 9).