Slope & Linear Equations (y = mx + b)
Aligned to 8.EE.B.6 — Common Core State Standards for Mathematics.
What this lesson teaches
Slope (m) is rise over run — how fast y changes as x changes. The y-intercept (b) is where the line crosses the y-axis. Together they define a line.
Worked examples
Example 1
Through (0, 2) and (3, 8): slope = (8−2)/(3−0) = 6/3 = 2. Intercept is 2, so y = 2x + 2.
Example 2
Through (1, 7) and (4, 1): slope = (1−7)/(4−1) = −6/3 = −2. Using y = −2x + b with (1, 7): 7 = −2 + b, so b = 9 and y = −2x + 9.
Example 3
A horizontal line has slope 0 (y = 3 never rises). A vertical line has undefined slope — the run is 0, and you cannot divide by 0.
Practice questions
- Find the slope between (1, 4) and (5, 12).
- Write the equation of a line with slope −3 through (0, 5).
- Graph y = (1/2)x − 1.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Pendiente y Ecuaciones Lineales (y = mx + b)
La pendiente (m) es el cambio vertical entre el cambio horizontal — qué tan rápido cambia y conforme cambia x. La intersección con el eje y (b) es donde la recta cruza el eje y. Juntas definen una recta.
Ejemplo 1: Por los puntos (0, 2) y (3, 8): pendiente = (8−2)/(3−0) = 6/3 = 2. La intersección es 2, entonces y = 2x + 2.
Ejemplo 2: Por (1, 7) y (4, 1): pendiente = (1−7)/(4−1) = −6/3 = −2. Usando y = −2x + b con (1, 7): 7 = −2 + b, así que b = 9 y y = −2x + 9.
Ejemplo 3: Una recta horizontal tiene pendiente 0 (y = 3 nunca sube). Una recta vertical tiene pendiente indefinida — el avance es 0, y no se puede dividir entre 0.
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