Investiguemos lo que las gráficas nos pueden decir acerca de las ecuaciones y las relaciones que ellas representan.
Student-Facing Targets
Entiendo que reescribir de distintas formas la ecuación de una recta puede hacer que sea más fácil encontrar cierto tipo de información sobre la relación y sobre su gráfica.
Puedo describir las relaciones que hay entre una ecuación de la forma , las características de su gráfica y la tasa de cambio de la situación.
Use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at .
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law to highlight resistance .
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).