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.
day 1 2 3 4 5 6 7 8 9 10
temperature (degrees F) 60 61 63 61 62 61 60 65 67 63

  1. What was the high temperature on Day 7?

  2. On which days was the high temperature 61 degrees?

  3. Is the high temperature a function of the day? Explain how you know.

  4. 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.

  1. 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.

  2. Is \(y\) a function of \(x\)? Explain how you know.

  3. 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.

Problem 4

Solve the system of equations: \(\begin{cases} y=7x+10 \\ y=\text-4x-23 \\ \end{cases}\)

(From Unit 5, Lesson 14.)