Linear Equations & Graphing

Slope-Intercept Form

y = mx + b
m = slope (rise/run), b = y-intercept (where line crosses y-axis)

y = 2x + 3: slope is 2, crosses y-axis at (0, 3)

m = (y₂ − y₁) / (x₂ − x₁)

Points (1, 2) and (3, 8): m = (8−2)/(3−1) = 6/2 = 3

y − y₁ = m(x − x₁) — useful when you know a point and slope

Slope 4, passes (2, 1): y − 1 = 4(x − 2) → y = 4x − 7

Ax + By = C where A, B, C are integers. Useful for finding intercepts quickly.
x-intercept: set y = 0. y-intercept: set x = 0.

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (m₁ × m₂ = −1).

Slope 2 → perpendicular slope = −1/2

What does a slope of 0 mean? Horizontal line — no rise.

What is an undefined slope? Vertical line — you can't divide by zero run.

Test what you just learned. Choose the best answer for each question.