Three Forms
The Three Main Forms
Slope-Intercept: y = mx + b
(m = slope, b = y-intercept)
Point-Slope: y − y₁ = m(x − x₁)
(m = slope, point (x₁, y₁) on the line)
Standard Form: Ax + By = C
(A, B, C are integers; A ≥ 0)
Slope-Intercept
y = mx + b
This is the most common form. You can read off the slope (m) and y-intercept (b) immediately.
y = 3x + 2 → slope = 3, y-intercept = (0, 2)
y = −x + 5 → slope = −1, y-intercept = (0, 5)
y = 2x → slope = 2, y-intercept = (0, 0)
Point-Slope
y − y₁ = m(x − x₁)
Use this when you know the slope and ONE point on the line (not necessarily the y-intercept).
Example: Write the equation of the line with slope 4 through the point (2, 7).
1. y − y₁ = m(x − x₁)
2. y − 7 = 4(x − 2)
3. Simplify: y − 7 = 4x − 8
4. y = 4x − 1 (slope-intercept form)
Converting Forms
Finding the Equation from Two Points
Find the equation through (1, 2) and (3, 8).
1. Find slope: m = (8−2)/(3−1) = 6/2 = 3
2. Use point-slope with (1, 2):
3. y − 2 = 3(x − 1)
4. y − 2 = 3x − 3
5. y = 3x − 1
Your Turn
Try It Yourself
Q1. Write in slope-intercept form: slope = −2, y-intercept = 5.
Show Answer
y = −2x + 5
Q2. Find the equation through (0, 3) and (4, 11).
Show Answer
m = (11−3)/(4−0) = 8/4 = 2
y-intercept = 3 → y = 2x + 3
Key Takeaways
1-Minute Summary
- Slope-intercept: y = mx + b — best for graphing
- Point-slope: y − y₁ = m(x − x₁) — best when you have a point + slope
- Given two points: find slope first, then use point-slope form