The effect of the sign of the slope in y = ax

A linear function is a function whose equation is of the form y = ax + b. We separate the discussion about it into two parts: b = 0 and b \neq 0. In this post, we only discuss the graph of y = ax + b where b = 0. We discuss the effect of the sign of the slope in y = ax.

If we let b = 0, the equation y = ax + b becomes y = ax + 0 or simply y = ax.

Notice that if x = 0, then y = ax = a(0) = 0. This means that the graph contains the point with coordinates (0,0). Therefore, y = ax passes through the origin.

Generalization 1: The graph y = ax passes through the origin.

We now examine the effect of the values of a. There are three cases: a = 0, a > 0, and a < 0» Read more

GeoGebra Tutorial Updates

For the past two months, I have been slowly updating my GeoGebra tutorials for GeoGebra 5.0. Several of the new updates include the series on GeoGebra Essentials.  The updates of other tutorial series will follow in the next few weeks.

Due the busy schedule and the installation of security features due to recent hacks, I have not posted for almost two weeks. However, this blog has more than 1000 posts, so you have more than enough to read. You might also want to take a look at Math and Multimedia’s 50 most popular posts. You can also to explore the different categories at the top of the page.

Below are some recent posts of Math and Multimedia:

Enjoy reading!

Mathematical Tasks: Number of Solutions and Answers

Different types of mathematical tasks let us tests the various skills of students. Close ended tasks let us test students basic knowledge of facts and procedures, while open-ended tasks lets us elicit various solutions answers. In the book Mathematical Thinking, Isoda and Katagiri classified mathematical tasks into three types:

Type 1: one solution, one answer

Type 2: many solutions, one answer

Type 3: many solutions, many answers

Examples of such problems are shown below. The first task is a Type 1 task, or a task with one solution and one answer. Students who have already learned how to calculate the area of rectangles can just use the formula to calculate the area of the rectangle.  » Read more

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