Lesson 8
Using Graphs to Compare Relationships
Let’s graph more than one relationship on the same grid.
Problem 1
The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).
__________________ vs volume
![Graph of points on coordinate plane, origin O.](https://staging-cms-im.s3.amazonaws.com/yLRkVa31GvVxPFPMmnjYuFzZ?response-content-disposition=inline%3B%20filename%3D%227-7.2.E.PP.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.E.PP.Image.10.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d96322bec96c92026660dff6984ca70a40cd32a3b7517e92b2457b1e413043a2)
_____________________ vs volume
![Graph of points on coordinate plane, origin O.](https://staging-cms-im.s3.amazonaws.com/fsenBttzN9Nqqr5GfA3JH4CW?response-content-disposition=inline%3B%20filename%3D%227-7.2.E.PP.Image.11.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.E.PP.Image.11.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3c43caab8bf7c8a0783b500a5f2175f892bab19ccc42680f63201dacf33b5c0f)
- Which graph is which? Give them the correct titles.
- Which quantities appear to be in a proportional relationship? Explain how you know.
- For the proportional relationship, find the constant of proportionality. What does that number mean?
Problem 2
Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes.
- Draw a graph with two lines that represent the bike rides of Lin and Andre.
- For each line, highlight the point with coordinates \((1,k)\) and find \(k\).
- Who was biking faster?
Problem 3
Match each equation to its graph.
- \(y = 2x\)
- \(y = \frac45 x\)
- \(y = \frac14 x\)
- \(y = \frac23 x\)
- \(y = \frac43 x\)
- \(y = \frac32 x\)
1
![Graph of a linear function, origin O.](https://staging-cms-im.s3.amazonaws.com/r3ba1ZWBYSGKQQ2SD7jZAczQ?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.07.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5ef42f200cfbcd3870d30cb03e93526e4856a4ea3937f7b56592067882798e93)
2
![Graph of a linear function, origin O.](https://staging-cms-im.s3.amazonaws.com/sdqCv7iEZSnPDh56Bix9GpTr?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.08.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6845ca80e4a1b5ebbced3538773835ca822cbdc284565d35f14f8018fa6404ca)
3
![Graph of a linear function, origin \(O\).](https://staging-cms-im.s3.amazonaws.com/kNzh7TJAb3gK64G13VnqinfF?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.09.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.09.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c654aa216f34a499d6037c8c01001890cb2b84b93290055294915a469a4b1e07)
4
![Graph of a linear function, origin O.](https://staging-cms-im.s3.amazonaws.com/4MqnAajWEeg4rVPrwHE3Jczm?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.10.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a1906910efb98bf92d8e324c1dcf9b55f4d98bbd31c47b14f4fb54df1da684a4)
5
![Graph of a linear function, origin O.](https://staging-cms-im.s3.amazonaws.com/XEbpdJ3eWpn7uiDrPtzRVfYg?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.11.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.11.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3753d1437e8474c775b3f079e556e57acc5f17f6d8192b2df203a8231c51f473)
6
![Graph of a linear function, origin O.](https://staging-cms-im.s3.amazonaws.com/esdeNuoKCqSTtgV9DyCWDosR?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.12.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.12.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=20240722T142414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a68077ea28023792bc3b58db6b3f80e2885eb08c2f3578da9cbe8f8a0592552e)