Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![The task is to find the rate of change of the linear function represented in the table below:
| x | y |
|---|----|
| 1 | 18 |
| 3 | 4 |
| 7 | -24|
In this table, the x-values signify the independent variable, while the y-values indicate the dependent variable for a linear function. The goal is to calculate the rate of change, which is equivalent to the slope of the line.
To calculate the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using (1, 18) and (3, 4) as an example:
\[ \text{slope} = \frac{4 - 18}{3 - 1} = \frac{-14}{2} = -7 \]
The same slope should result from using any two points, confirming the function is linear.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F357bbc30-b0f0-4565-8f69-aa69d6b38b7e%2F94a61e36-a3b6-4309-b9e0-db90083bfc3f%2Fjudppcr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to find the rate of change of the linear function represented in the table below:
| x | y |
|---|----|
| 1 | 18 |
| 3 | 4 |
| 7 | -24|
In this table, the x-values signify the independent variable, while the y-values indicate the dependent variable for a linear function. The goal is to calculate the rate of change, which is equivalent to the slope of the line.
To calculate the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using (1, 18) and (3, 4) as an example:
\[ \text{slope} = \frac{4 - 18}{3 - 1} = \frac{-14}{2} = -7 \]
The same slope should result from using any two points, confirming the function is linear.
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