Analyzing Graphs Qualitatively
Aligned to 8.F.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
A graph tells a story: going up means increasing, going down means decreasing, and flat means constant. Steepness shows how fast the change is; straight sections are linear and curved sections are nonlinear.
Worked examples
Example 1
A graph of the water in a tub rises steeply while it fills, stays flat (level) while someone bathes, then drops to zero as it drains. The flat part shows the amount is constant; the steep drop shows a fast decrease.
Example 2
A graph of a car's distance from home rises, flattens during a stop, then falls as it returns. A flat stretch means no change, not zero distance.
Example 3
Steeper means faster. Two rising sections with different slopes tell you where the car sped up without any numbers on the axes.
Practice questions
- Describe what a flat horizontal section of a distance-time graph means.
- Sketch a graph of a runner speeding up, then resting, then slowing to a stop.
- A graph rises, then falls, then rises again — describe a real situation it could model.
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
Análisis Cualitativo de Gráficas
Una gráfica cuenta una historia: subir significa aumentar, bajar significa disminuir y estar plana significa constante. La inclinación muestra qué tan rápido es el cambio; los tramos rectos son lineales y los tramos curvos son no lineales.
Ejemplo 1: Una gráfica del agua en una tina sube abruptamente mientras se llena, se mantiene plana (nivelada) mientras alguien se baña, y luego cae a cero al vaciarse. La parte plana muestra que la cantidad es constante; la caída abrupta muestra una disminución rápida.
Ejemplo 2: Una gráfica de la distancia de un coche a su casa sube, se aplana durante una parada y luego baja al regresar. Un tramo plano significa que no hay cambio, no distancia cero.
Ejemplo 3: Más inclinado significa más rápido. Dos tramos que suben con distinta pendiente te dicen dónde aceleró el coche sin números en los ejes.
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