Lesson 17
Four Representations
Problem 1
The equation \(c = 2.95g\) shows how much it costs to buy gas at a gas station on a certain day. In the equation, \(c\) represents the cost in dollars, and \(g\) represents how many gallons of gas were purchased.
- Write down at least four (gallons of gas, cost) pairs that fit this relationship.
- Create a graph of the relationship.
- What does 2.95 represent in this situation?
- Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct? How did she come up with that?
Solution
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Problem 2
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, as shown in the graph.
- Plot and label at least two more points that represent the relationship.
- Use a straightedge to draw a line that represents this proportional relationship.
- For which value y is (\(1, y\)) on the line you just drew?
- What is the constant of proportionality for this relationship?
- Write an equation representing this relationship. Use \(c\) for cups and \(t\) for tablespoons.
![Graph of a point on coordinate plane, origin O. Horizontal axis, volume in cups, scale 0 to 6, by 1’s. Vertical axis, volume in tablespoons, scale 0 to 70, by 10’s. Point at (3 comma 48).](https://cms-im.s3.amazonaws.com/ZB72xgWJjZgiYK1VE7SmrFD4?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T202848Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7c888f236828066ef5d27034e38623846dcb11a70c244fa5a8bb22dd028e476d)
Solution
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