Lesson 12
Using Graphs to Compare Relationships
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f0ec6bd578509a8b5de3652c25e7229ff132d558c380fde6d3f175675f677ecd)
_____________________ 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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=98863a8a1b6d37da69e8b4515e17eba4bd4939ba239c6226041196a5be6d57e5)
- 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?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
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?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f55b3500b0685283a807d2e7a7a3e1aa1a9824547db3fc907d01fa1bd099cfb1)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e3a189119f9e2c387112029dc385f9488d285167de75571605a32c25294843f8)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=16cb34ffb74daa48b1e7e34ec99f9bbfac566c509aee9425bc90103b8c7aab15)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3d697e6296df1d47780e8971e2b0201e1b608303227e9c97435f2d608ddbb7cf)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=52748aad113f45f43c6f6ff12522a1e173e76acdc75a7ebbb256d1bebadca368)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=47d781921bdcbcaf08899b66ddb63d7b146126986edf77d93c552d94caae082c)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.