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 exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Question
![### Exercise 3.4, Question 71 (Page 227)
**Problem Statement:**
Find the slope of the line and the y-intercept, and write the equation of the line in slope-intercept form.
**Graph Analysis:**
The graph displays a straight line plotted on a coordinate grid. The axes are labeled with numbers ranging from -10 to 10 on both the x-axis and the y-axis. The line passes through the origin (0,0) and has a positive slope.
**Slope and Y-Intercept:**
- **Slope (m):** To determine the slope, observe the change in y-values versus the change in x-values between two points on the line. For every increase of 5 units in x, the line rises 5 units in y (using points like (0,0) and (5,5)). Slope \( m = \frac{\Delta y}{\Delta x} = \frac{5}{5} = 1 \).
- **Y-Intercept (b):** The y-intercept is where the line crosses the y-axis. Here, it is 0 since the line passes through the origin.
**Equation in Slope-Intercept Form (y = mx + b):**
Substituting the calculated slope and y-intercept into the slope-intercept form gives:
\[ y = 1x + 0 \]
or simply,
\[ y = x \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0f62ed3-8b4a-44c7-84cc-6b36e3c7df59%2F670576f8-e213-4e85-a6a4-ec848929eadc%2F6k55smj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exercise 3.4, Question 71 (Page 227)
**Problem Statement:**
Find the slope of the line and the y-intercept, and write the equation of the line in slope-intercept form.
**Graph Analysis:**
The graph displays a straight line plotted on a coordinate grid. The axes are labeled with numbers ranging from -10 to 10 on both the x-axis and the y-axis. The line passes through the origin (0,0) and has a positive slope.
**Slope and Y-Intercept:**
- **Slope (m):** To determine the slope, observe the change in y-values versus the change in x-values between two points on the line. For every increase of 5 units in x, the line rises 5 units in y (using points like (0,0) and (5,5)). Slope \( m = \frac{\Delta y}{\Delta x} = \frac{5}{5} = 1 \).
- **Y-Intercept (b):** The y-intercept is where the line crosses the y-axis. Here, it is 0 since the line passes through the origin.
**Equation in Slope-Intercept Form (y = mx + b):**
Substituting the calculated slope and y-intercept into the slope-intercept form gives:
\[ y = 1x + 0 \]
or simply,
\[ y = x \]
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