Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable things students can learn is to be able to visualize linear equations and systems of equations so that they can tell the quadrant where the intersection and therefore the solution is. This develops the valuable ability to estimate solutions. We suggest students practice picturing and then graphing systems with a variety of slopes and intercepts. Significant relationships like perpendicular lines should be another focus.
Tag: linear functions
Peter’s Taxi
There are a wide variety of financial literacy problems. This is the kind of problem that appears on many tests. It does not ask you directly to find the cost of a taxi ride which includes both a fixed and variable amount. See if you can use this Lab to make this problem and problems like it easy for you to solve.
Solving Equations
Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions and use them to solve equations. We treat an equation as the equality of two functions, graph each one and then look at their intersection. This is a powerful way to think about solving equations due to Judah Schwartz and one that we believe will help many student to understand this algebra.
Linear Functions
Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general form is f(x)=mx+b where m is the slope of the function and b is the y-intercept, the value where the line crosses the y-axis. This Lab is designed to give you a picture of a linear function based on its formula. So play with it until you can picture the function from its formula and its formula from its graph.