Solutions as Intersections
Aligned to A-REI.D.11 — Common Core State Standards for Mathematics.
What this lesson teaches
Where two graphs y = f(x) and y = g(x) cross, the x-value makes f(x) = g(x). So the intersection points give the solutions of the equation f(x) = g(x).
Worked example
Solve 2x + 1 = x + 4. The lines y = 2x + 1 and y = x + 4 meet where 2x + 1 = x + 4, so x = 3; then y = 7. They intersect at (3, 7).
Practice questions
- Solve x + 5 = 2x + 2 algebraically and state the intersection point.
- Two lines cross at (4, 9). What is the solution of f(x) = g(x)?
- Explain why the x-coordinate, not the y-coordinate, solves f(x) = g(x).
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
Soluciones como Intersecciones
Donde se cruzan dos gráficas y = f(x) y y = g(x), el valor de x hace f(x) = g(x). Así, los puntos de intersección dan las soluciones de la ecuación f(x) = g(x).
Ejemplo: Resuelve 2x + 1 = x + 4. Las rectas y = 2x + 1 y y = x + 4 se cruzan donde 2x + 1 = x + 4, así que x = 3; luego y = 7. Se cortan en (3, 7).
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