IM 8.3.7 Lesson: Representations of Linear Relationships

Which glass will hold the most water?

Which glass will hold the least water?

Move the green circle to set the starting water level. Record the new level after you drop each marble.

What is the volume, V, in the cylinder after you add:

3 objects?

7 objects?

objects? Explain your reasoning.

If you wanted to make the water reach the highest mark on the cylinder, how many objects would you need?

Plot and label points that show your measurements from the experiment.

  • Plot and label a point that shows the depth of the water before you added any objects.
  • The points should fall on a line. Use the Line tool to draw this line.
  • Compute the slope of the line using several different triangles.
Does it matter which triangle you use to compute the slope? Why or why not?

The equation of the line in the experiment has two numbers and two variables. What physical quantities do the two numbers represent?

What does  represent and what does  represent?

A situation is represented by the following equation:

  Invent a story for this situation.

Graph the equation

What do the and the represent in your situation?

Where do you see and on the graph?

For each graph, record:

Describe a procedure for finding the slope between any two points on a line.

Write an expression for the slope of the line in the graph using the letters  and .