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What's true about the first differences and slope for a linear equation?

What's true about the first differences and slope for a linear equation?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** What's true about the first differences and slope for a linear equation? **Text Box:** *The text box is currently empty, indicating this is meant for user input, perhaps for a discussion or as an exercise on an educational website.* **Explanation:** For a linear equation, the first differences represent the constant changes in the dependent variable (usually \(y\)) with respect to the independent variable (usually \(x\)). The slope of the linear equation, often denoted as \(m\) in the equation \(y = mx + b\), quantifies this constant rate of change. Thus, in a linear equation, both the first differences and the slope are constant.
Transcribed Image Text:**Question:** What's true about the first differences and slope for a linear equation? **Text Box:** *The text box is currently empty, indicating this is meant for user input, perhaps for a discussion or as an exercise on an educational website.* **Explanation:** For a linear equation, the first differences represent the constant changes in the dependent variable (usually \(y\)) with respect to the independent variable (usually \(x\)). The slope of the linear equation, often denoted as \(m\) in the equation \(y = mx + b\), quantifies this constant rate of change. Thus, in a linear equation, both the first differences and the slope are constant.
Expert Solution
Step 1

The slope-Intercept form of a line is  

y=mx+c where m is slope and c is the y-intercept.

The slope of the line is obtained as Let (x1,y1) and x2,y2 are the two points on the line then 

slope =y2-y1x2-x1

 

 

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