# Representations of Linear Relationships

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Establish a Linear Relationship From the Amount of Liquid Displaced by an Object.

• Move the green circle to set the starting water level. ​
• Drop a marble.
• Record the new level.
• Continue to record the new water level each time you drop a marble.

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

(1). 3 objects?

(2). 7 objects?

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

(5). 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.

(6). Does it matter which triangle you use to compute the slope? Why or why not?

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

(8). What does  V represent and what does  represent?

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Interprete and Graph a Linear Relationship.

A situation is represented by the following equation: .

(1). Invent a story for this situation.

(2). Graph the equation.

(3). What do the and 5 represent in this situation? and the represent in your situation?

(4). What do you find and 5 on the graph? and the represent in your situation?

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Create Graphs of Linear Relationships.

Create a graph that shows three linear relationships with different y-intercepts using the following slopes, and write an equation for each line.

(1). Equation for line 1:

(2). Equation for line 2:

(3). Equation for line 3:

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Here are recipes for two different banana cakes. Information for the first recipe is shown in the table.

(2). What is the constant of proportionality for each situation and what does it mean?

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The graph shows the height in inches, h, of a bamboo plant t months after it has been planted.

(1). Write an equation that describes the relationship between.

(2). After how many months will the bamboo plant be 66 inches tall? Explain or show your reasoning.

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(1). For each graph above, complete the table below:

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

and .