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Find the rate of change of the linear function in the table. X 1 3. 7 y 18 4 -24

Find the rate of change of the linear function in the table. X 1 3. 7 y 18 4 -24

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.6: Relations
Problem 2BGP
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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.
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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