3.4 Exercise question 71 page 227. Find the slope of the line and the y-intercept and write the equation of the 10 -5- -10 -5 10 -5- -10

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
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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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### 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,
\[ y = x \]
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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