Lesson 9
Two Graphs for Each Relationship
Let’s use tables, equations, and graphs to answer questions about proportional relationships.
Problem 1
At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40.
- How much does honey cost per ounce?
- How much honey can you buy per dollar?
- Write two different equations that represent this situation. Use \(h\) for ounces of honey and \(c\) for cost in dollars.
![A blank coordinate plane.](https://staging-cms-im.s3.amazonaws.com/jnLpYT9fswbgSfr6agRWC5hs?response-content-disposition=inline%3B%20filename%3D%227-7.2.F2.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F2.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T142600Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bc8c81b057f8c50e6c7c3e57e4a19df9afeebcfa88724eff435b07a7073ce484)
- Choose one of your equations, and sketch its graph. Be sure to label the axes.
Problem 2
The point \((3, \frac65)\) lies on the graph representing a proportional relationship. Which of the following points also lie on the same graph? Select all that apply.
\((1, 0.4)\)
\((1.5, \frac{6}{10})\)
\((\frac65, 3)\)
\((4, \frac{11}{5})\)
\((15, 6)\)
Problem 3
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, \(r\) (cups), and the amount of peanuts, \(p\) (cups), in this recipe.
- Write the equation for the relationship that has constant of proportionality greater than 1. Graph the relationship.
- Write the equation for the relationship that has constant of proportionality less than 1. Graph the relationship.
Problem 4
Here is a graph that represents a proportional relationship.
- Come up with a situation that could be represented by this graph.
- Label the axes with the quantities in your situation.
- Give the graph a title.
- Choose a point on the graph. What do the coordinates represent in your situation?
![Graph of a line on a coordinate plane, origin O. Horizontal axis has scale 0 to 50 by 5’s. Vertical axis has scale 0 to 100 by 10’s. The line begins at (0 comma 0) and goes through (110 comma 55).](https://staging-cms-im.s3.amazonaws.com/cFXkGhhbDt3axP5agQCA1LpX?response-content-disposition=inline%3B%20filename%3D%227-7.2.D11.Image.Revision.130.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.D11.Image.Revision.130.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T142600Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad931ba54aa2bed1560ecfdfd885d0af302bd2fcdb6e781fd6e67ce709022a24)