A system of linear equations consists of multiple linear equations. You can think of this as multiple lines graphed on one coordinate plane. Three situations can arise when looking at such a graph. Either:1) No point(s) are shared by all lines shown2) There is one point that all lines cross through3) The lines lie on top…… Continue reading Linear Systems: Why Does Linear Combination Work (Graphically)?
How to recognize vertical and horizontal dilations in both graphs and equations.
How to determine both vertical and horizontal translation factors (relative to a “parent function”) when looking the definition of a function.
A few more interactive GeoGebra applets have been added to my collection. Each of these graphs the function indicated in the name, with parameters that you can adjust using sliders. As you move a slider, you can watch how that parameter affects the graph of the function, and see what the resulting function definition looks…… Continue reading Interactive Graphs for Exponential and Logarithmic Functions
A list of GeoGebra applets that help students better understand the relationship between the coefficients in an equation and the corresponding graph.
The following equations all have a similarity: $latex y = |x – 8| + 5\\*~\\*y = 4(x – 6) – 7\\*~\\*(x – 3)(13x + 11) = 0\\*~\\*y = (x + 1)^2 – 9&s=2&bg=ffffff&fg=000000$ The similarity is that they all have expressions like (x- 6) or (13x + 11), which are often either translations or factors.…… Continue reading Keep Your Eye On The Variable
Explanation of key linear equation concepts: slope, intercepts, and equation forms. Discussion of how slope-intercept form, point-slope form, and standard form are related to one another. Includes general descriptions of the various starting points a student is likely to encounter in problems, and how to proceed from there.