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,...
Related questions
Question
![**Linear Function Analysis**
**Question 30:**
The graph of a linear function, \( f \), is given.
**Tasks:**
(a) The slope is _______
(b) The y-intercept is _______
(c) The function for this graph is _______
**Graph Explanation:**
The graph is a straight line displayed on a Cartesian plane. It has the following characteristics:
- The x-axis is marked with integers ranging from -2 to 4.
- The y-axis is marked with integers ranging from -4 to 8.
- The line crosses the y-axis at \( y = 2 \).
- The line ascends to the right, indicating a positive slope.
To determine the slope, identify two points on the line. For instance, using the points (0, 2) and (2, 4), the slope \( m \) can be calculated as:
\[ m = \frac{4 - 2}{2 - 0} = 1 \]
The y-intercept is the point where the line crosses the y-axis; in this case, it is \( y = 2 \).
The linear function can be expressed in the slope-intercept form \( y = mx + b \). Therefore, the function is:
\[ y = 1x + 2 \] or simply \( y = x + 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2860bcf7-9e8d-460b-a0cf-53a1e326bc6d%2Fd1ff8378-2b96-4c46-96b0-6833c92ba7f6%2F6ouqrdh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Linear Function Analysis**
**Question 30:**
The graph of a linear function, \( f \), is given.
**Tasks:**
(a) The slope is _______
(b) The y-intercept is _______
(c) The function for this graph is _______
**Graph Explanation:**
The graph is a straight line displayed on a Cartesian plane. It has the following characteristics:
- The x-axis is marked with integers ranging from -2 to 4.
- The y-axis is marked with integers ranging from -4 to 8.
- The line crosses the y-axis at \( y = 2 \).
- The line ascends to the right, indicating a positive slope.
To determine the slope, identify two points on the line. For instance, using the points (0, 2) and (2, 4), the slope \( m \) can be calculated as:
\[ m = \frac{4 - 2}{2 - 0} = 1 \]
The y-intercept is the point where the line crosses the y-axis; in this case, it is \( y = 2 \).
The linear function can be expressed in the slope-intercept form \( y = mx + b \). Therefore, the function is:
\[ y = 1x + 2 \] or simply \( y = x + 2 \).
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