Embedded Files
Learning Targets
- I understand the information given by graphs of proportional relationships that are made of up of points or a line.
- I can find the constant of proportionality from a graph.
- I can draw the graph of a proportional relationship given a single point on the graph (other than the origin).
Notes
Notes
For the relationship represented in this table, y is proportional to x. We can see in the table that (5/4) is the constant of proportionality because it’s the y value when x is 1.
The equation y=(5/4)x also represents this relationship.
Here is the graph of this relationship.
If y represents the distance in feet that a snail crawls in x minutes, then the point (4,5) tells us that the snail can crawl 5 feet in 4 minutes.
If y represents the cups of yogurt and x represents the teaspoons of cinnamon in a recipe for fruit dip, then the point (4,5) tells us that you can mix 4 teaspoons of cinnamon with 5 cups of yogurt to make this fruit dip.
We can find the constant of proportionality by looking at the graph, because (5/4) is the y-coordinate of the point on the graph where the x-coordinate is 1. This could mean the snail is traveling (5/4) feet per minute or that the recipe calls for 1¼ cups of yogurt for every teaspoon of cinnamon.
In general, when y is proportional to x, the corresponding constant of proportionality is the y-value when x = 1.
Activities
Activities
11.2 Tyler's Walk
11.2 Tyler's Walk
Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.
- The point on the graph shows his arrival at the bumper cars. What do the coordinates of the point tell us about the situation?
- The table representing Tyler's walk shows other values of time and distance. Complete the table. Next, plot the pairs of values on the grid.
- What does the point (0,0) mean in this situation?
- How far away from the ticket booth was Tyler after 1 second? Label the point on the graph that shows this information with its coordinates.
- What is the constant of proportionality for the relationship between time and distance? What does it tell you about Tyler's walk? Where do you see it in the graph?
11.3 Seagulls Eat What?
11.3 Seagulls Eat What?
4 seagulls ate 10 pounds of garbage. Assume this information describes a proportional relationship.
- Plot a point that shows the number of seagulls and the amount of garbage they ate.
- Use a straight edge to draw a line through this point and (0,0).
- k represents the constant of proportionality What is k? What does the value of k tell you about this context?
- Plot the point (1, k) on the line. What do you notice?
Questions & Answers to Ponder...
- Is it possible to interpret the meaning of every point on the solid line? (No, only whole numbers of seagulls make sense.)
- Why is it still useful to draw the line, even if we can’t interpret every point? (Yes! It helps us see the pattern and visualize the situation.)
- How can drawing the line help us learn more about the situation? (It helps us to easily find out how much garbage different numbers of seagulls eat. It also helps us to estimate the value of k.)
Summary
Summary
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