Based on the graph of this line, write a linear equation that is incorrect. Next, write a linear equation that could be correct.

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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  • Based on the graph of this line, write a linear equation that is incorrect. Next, write a linear equation that could be correct.

 

 

**Instructions:**
Based on the graph of this line, write a linear equation that could be correct.

**Graph Description:**
The graph depicts a line plotted on a standard Cartesian coordinate system. The line passes through the following points:
1. Approximately (0, -2) on the y-axis.
2. Another point around (2, 1).
3. Another point around (4, 4).

The line has a positive slope, indicating that it ascends as it moves from left to right.

**Possible Linear Equation:**
To write a linear equation, use the slope-intercept form: \(y = mx + b\).

**Calculating the Slope (m):**
- Choose two points: (0, -2) and (2, 1).
- Slope \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{2 - 0} = \frac{3}{2}\).

**Identifying the y-intercept (b):**
- The line crosses the y-axis at -2.

**Equation:**
With a slope of \(\frac{3}{2}\) and a y-intercept of -2, one possible equation for the line is:
\[ y = \frac{3}{2}x - 2\]

This is one linear equation that fits the graph.
Transcribed Image Text:**Instructions:** Based on the graph of this line, write a linear equation that could be correct. **Graph Description:** The graph depicts a line plotted on a standard Cartesian coordinate system. The line passes through the following points: 1. Approximately (0, -2) on the y-axis. 2. Another point around (2, 1). 3. Another point around (4, 4). The line has a positive slope, indicating that it ascends as it moves from left to right. **Possible Linear Equation:** To write a linear equation, use the slope-intercept form: \(y = mx + b\). **Calculating the Slope (m):** - Choose two points: (0, -2) and (2, 1). - Slope \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{2 - 0} = \frac{3}{2}\). **Identifying the y-intercept (b):** - The line crosses the y-axis at -2. **Equation:** With a slope of \(\frac{3}{2}\) and a y-intercept of -2, one possible equation for the line is: \[ y = \frac{3}{2}x - 2\] This is one linear equation that fits the graph.
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