Discovering Relationships in Lines through the Origin

Let's experiment some more.

Use this online graphing calculator to perform your experiments. Keep a record of the things you learn about lines that go through the origin (0, 0) and their equations.

On the graphing calculator, next to the red square, there is y1 = then an empty box. In the box, type 1x. Click on the orange Graph button. The calculator will graph y = 1x. Write down a description of what the graph looks like. Be specific.

Without deleting the x from the first box, in the box next to y2 = type 2x. Click on Graph. The calculator will graph y = 1x and y = 2x. How is the new graph different from the old one?

Without deleting anything from the boxes, in the box next to y3 = type 5x. How is this graph different from the first two? What is the equation of this graph we just added?

What do you think will happen if we type in 7x in the last box? What is the equation of this graph we just added?

Check to see if you were right.

What do you think will happen if we type in 1/2x in the last box?

In the last box, delete the 7x and type in 1/2x. Check to see if your answer was right. The equation of this graph is y = 1/2x.

Experiment by changing the number in front of the x (this is called the coefficient of x) to other fractions. Continue experimenting until you can figure out what the graph of the equation will look like without having to graph it.

Now, experiment with changing the coefficient of x to negative numbers. Continue experimenting until you can figure out what the graph of the equation will look like without having to graph it.

Carefully examine all these lines through the origin. Then, upload your comment about this topic:

If you begin with the graph y = 1x, what happens if you change the number 1 to a higher number? What happens if you change it to a fraction? What happens if you change it to a negative number?