![]() Instead of solving by graphing, we can solve the system algebraically. ![]() In explaining their strategies, students need to be precise in their word choice and use of language (MP6).īecause the warm-up is intended to promote reasoning, discourage the use of graphing technology to graph the systems. To match graphs and equations, students need to look for and make use of structure (MP7) in both representations. The solution (if there is one) to this system would have to have -5 for the \(x\)-value. The intersection of the given graphs is a point to the right of the vertical axis (and therefore having a positive \(x\)-value), so the graphs cannot represent that system. For instance, given a system with \(x=\text-5\) as one of the equations, they may reason that any point that has a negative \(x\)-value will be to the left of the vertical axis. Those who don't recall it can still reason about the system structurally. In the last system, a simple rearrangement to one equation would put it in this form.) Activating this knowledge would enable students to quickly tell whether a system matches the given graphs. (In each of the first three systems, one equation is already in this form. Some students may remember that the equation for such lines can be written as \(x = a\) or \(y=b\), where \(a\) and \(b\) are constants. The equations presented and the reasoning elicited here will be helpful later in the lesson, when students solve systems of equations by substitution.Īll four systems include an equation for either a horizontal or a vertical line. ![]() Given two graphs on an unlabeled coordinate plane, students must rely on what they know about horizontal and vertical lines, intercepts, and slope to determine if the graphs could represent each pair of equations. This Math Talk encourages students to look for connections between the features of graphs and of linear equations that each represent a system.
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