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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f22e931fbb32a96c11380dbdd8e8177476631441a18c320b80474e398a2ce7bd)
_____________________ vs volume
![Graph of points on coordinate plane, origin O.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=651fe0f251142bc430ce88846c9411d23a73403b15898982e1ccd6e952222f67)
- 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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2973eefb9bf5ecc63bb43706b26a6d2f9ee7f5cbb54a36d2db1367cbba9c4631)
2
![Graph of a linear function, origin O.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0dd47c7d342f8cad224d714db4acdf98025c79591d1dcd8ef7f41d58cd73672a)
3
![Graph of a linear function, origin \(O\).](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a9248e5e0dc95075397deb760971925b55b718caa7e75a39a1ec8025a8422d01)
4
![Graph of a linear function, origin O.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8550bbc97d199ff0605d902d3b6013e83d165d9e2abde78845f3db5fed70fc1e)
5
![Graph of a linear function, origin O.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8d4b99d23f198e59ef869da4665c719dca700227eb9345c3f5094b94eb6e5531)
6
![Graph of a linear function, origin O.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T033253Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4995050cf19c887719c3c18bc7facf7aa4104e6bd8531dfba6fa8eaaab04c330)