Lesson 8
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=25e2f7b2affcbee8e20a220e3da26f26ef3c36c73f9cec8aba9281e5dce762f7)
_____________________ 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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cee79d1f8d9484b188c5fe011abc94171fb04ed7b5d28f6696689930b2621ef7)
- 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
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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
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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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=da812d0d4282e609ada73049ad13063dc4b4ccf2dd738f6542dee196ab66b287)
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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=63e24379765b7ad502f4dbfec2c5450229dd8e06b67cd47b1e3233b1053cae70)
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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1fc29bd28ba4401dd7f4d2ca8b38fd88b761db53e88f956735882e40c81faf14)
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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c13fa9a36e1f5e4a7cf24105a83bbf7396396504955359ac7dcf48727d2184a5)
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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6fc8b6ec3237500623a70be1e97f36d855773f442aa6427ea32ac1f8695d8074)
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=20240727T003826Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=68cae78646215bf574b5cb1c3a1450e107bc98ae9a31e47a5fba845dc1daa335)
Solution
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