Representing Proportional Relationships

Move the LARGE SLIDER (at the bottom) slowly to create various scenarios. Answer the question below.

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Explore Ways to Represent Linear Situations

(A). Here are two ways to represent a situation.

(1). Create a table that represents this situation with at least 3 pairs of values.

(2). Graph this relationship and label the axes.

(3). How can you see or calculate the constant of proportionality in each representation? What does it mean?

(4). Explain how you can tell that the equation, description, graph, and table all represent the same situation.

(B). Here are two ways to represent a situation.

(1). Write an equation that represents this situation. (Use c to represent number of cars and use m to represent amount raised in dollars.)

(2). Graph this relationship and label the axes.

(3). How can you see or calculate the constant of proportionality in each representation? What does it mean?

(4). Explain how you can tell that the equation, description, graph, and table all represent the same situation.

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Write a Linear Equation From a Graph.

Here is a graph of the proportional relationship between calories and grams of fish:

(1). Write an equation that reflects this relationship using to represent the amount of fish in grams and to represent the number of calories.

(2). Use your equation to complete the table:

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Writing an Equation That Represents a Linear Relationship.

Students are selling raffle tickets for a school fundraiser. They collect $24 for every 10 raffle tickets they sell. Suppose M is the amount of money the students collect for selling R raffle tickets.

(1). Write an equation that reflects the relationship between M and R.

(2). Using the graph below, label and scale the axes and graph this situation with M on the vertical axis and R on the horizontal axis. (Make sure the scale is large enough to see how much they would raise if they sell 1000 tickets.)

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(1). A line ir represented by the equation What are the coordinates of some points that lie on the line?

(2). Graph the line below.

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Ten people can dig five holes in three hours. If n people working at the same rate dig m holes in d hours:

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Describe how you can tell whether a line’s slope is greater than 1, equal to 1, or less than 1.