Lesson 4
Tables, Equations, and Graphs of Functions
Let’s connect equations and graphs of functions.
Problem 1
The graph and the table show the high temperatures in a city over a 10-day period.
![Coordinate plane, day, 1 to 10, high temperature, degrees F, 59 to 69. Points, 1 comma 60, 2 comma 61, 3 comma 63, 4 comma 61, 5 comma 62, 6 comma 61, 7 comma 60, 8 comma 65, 9 comma 67, 10 comma 63.](https://cms-im.s3.amazonaws.com/XxhdqiBRMSwvbUFMMQ8utWxA?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.B.Image.13.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.B.Image.13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163237Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e1e1cb9b1704f1509239b9b00bb7bf7e30a5344419c425bc6ede702652d2eda1)
day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
temperature (degrees F) | 60 | 61 | 63 | 61 | 62 | 61 | 60 | 65 | 67 | 63 |
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What was the high temperature on Day 7?
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On which days was the high temperature 61 degrees?
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Is the high temperature a function of the day? Explain how you know.
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Is the day a function of the high temperature? Explain how you know.
Problem 2
The amount Lin’s sister earns at her part-time job is proportional to the number of hours she works. She earns $9.60 per hour.
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Write an equation in the form \(y=kx\) to describe this situation, where \(x\) represents the hours she works and \(y\) represents the dollars she earns.
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Is \(y\) a function of \(x\)? Explain how you know.
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Write an equation describing \(x\) as a function of \(y\).
Problem 3
Use the equation \(2m+4s=16\) to complete the table, then graph the line using \(s\) as the dependent variable.
\(m\) | 0 | -2 | ||
---|---|---|---|---|
\(s\) | 3 | 0 |
![Blank coordinate plane. x, negative 6 to 10 by ones, y, negative 4 to 10 by ones.](https://cms-im.s3.amazonaws.com/tSmkiRSh8RnHvFiNuv7CsuPt?response-content-disposition=inline%3B%20filename%3D%228-8.5.B4.PP.Image.103.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B4.PP.Image.103.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163237Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=45e0957a3c7e2ebd3246cc1981375b17ec889e10ff8a4ba1e614b8ab33c3c700)
Problem 4
Solve the system of equations: \(\begin{cases} y=7x+10 \\ y=\text-4x-23 \\ \end{cases}\)