Graphs as Solution Sets
Aligned to A-REI.D.10 — Common Core State Standards for Mathematics.
What this lesson teaches
Every point (x, y) on the graph of an equation makes the equation true, and every point off the graph makes it false. The line or curve is the picture of all solutions.
Worked examples
Example 1
Does (2, 7) lie on y = 3x + 1? Substitute: 3(2) + 1 = 7. Since 7 = 7, the point is a solution and lies on the line.
Example 2
Every point on the line is a solution and every solution is on the line. That equivalence is what a graph is.
Example 3
A curve works the same way. (3, 9) is on y = x² because 3² = 9, and being 'close' to the curve is not being on it.
Practice questions
- Is (1, 5) on the line y = 4x + 1?
- Is (0, −2) on the line y = 2x − 2?
- Find one more point on y = x + 3 besides (0, 3).
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
Las Gráficas como Conjuntos Solución
Cada punto (x, y) sobre la gráfica de una ecuación la hace verdadera, y todo punto fuera de la gráfica la hace falsa. La recta o curva es el dibujo de todas las soluciones.
Ejemplo 1: ¿(2, 7) está en y = 3x + 1? Sustituye: 3(2) + 1 = 7. Como 7 = 7, el punto es solución y está sobre la recta.
Ejemplo 2: Todo punto de la recta es solución y toda solución está en la recta. Esa equivalencia es lo que es una gráfica.
Ejemplo 3: Una curva funciona igual. (3, 9) está en y = x² porque 3² = 9, y estar 'cerca' de la curva no es estar en ella.
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