### Question 6: **Task:** Write 3 different equations that represent the line shown on the graph. **Graph Description:** - The graph displays a coordinate plane with the x-axis labeled from -5 to 5 and the y-axis labeled from -4 to 4. - The line is plotted through points on the graph and specifically passes through two points: (0, 4) and (3, -2). - The line has a negative slope and is decreasing from left to right across the plane. **Equations:** 1. **Slope-Intercept Form: \( y = mx + b \)** - The slope-intercept form equation is given as: ``` y = -2x + 4 ``` - This form uses the slope (m = -2) and the y-intercept (b = 4). 2. **Point-Slope Form: \( y - y_1 = m(x - x_1) \)** - The point-slope form equation is given using a point (1, 2): ``` y - 2 = -2(x - 1) ``` - This form emphasizes the slope (m = -2) and a specific point on the line. 3. **Standard Form: \( Ax + By = C \)** - The standard form equation is expressed as: ``` 2x + y = 4 ``` - This format rearranges the linear equation into a standardized algebraic form where A, B, and C are integers. **Note:** Each form is a valid representation of the same line on the graph, showcasing different approaches to expressing linear equations.
### Question 6: **Task:** Write 3 different equations that represent the line shown on the graph. **Graph Description:** - The graph displays a coordinate plane with the x-axis labeled from -5 to 5 and the y-axis labeled from -4 to 4. - The line is plotted through points on the graph and specifically passes through two points: (0, 4) and (3, -2). - The line has a negative slope and is decreasing from left to right across the plane. **Equations:** 1. **Slope-Intercept Form: \( y = mx + b \)** - The slope-intercept form equation is given as: ``` y = -2x + 4 ``` - This form uses the slope (m = -2) and the y-intercept (b = 4). 2. **Point-Slope Form: \( y - y_1 = m(x - x_1) \)** - The point-slope form equation is given using a point (1, 2): ``` y - 2 = -2(x - 1) ``` - This form emphasizes the slope (m = -2) and a specific point on the line. 3. **Standard Form: \( Ax + By = C \)** - The standard form equation is expressed as: ``` 2x + y = 4 ``` - This format rearranges the linear equation into a standardized algebraic form where A, B, and C are integers. **Note:** Each form is a valid representation of the same line on the graph, showcasing different approaches to expressing linear equations.
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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Can you guys pleasss help !! What's the answer for those 3 ?
Transcribed Image Text:### Question 6:
**Task:**
Write 3 different equations that represent the line shown on the graph.
**Graph Description:**
- The graph displays a coordinate plane with the x-axis labeled from -5 to 5 and the y-axis labeled from -4 to 4.
- The line is plotted through points on the graph and specifically passes through two points: (0, 4) and (3, -2).
- The line has a negative slope and is decreasing from left to right across the plane.
**Equations:**
1. **Slope-Intercept Form: \( y = mx + b \)**
- The slope-intercept form equation is given as:
```
y = -2x + 4
```
- This form uses the slope (m = -2) and the y-intercept (b = 4).
2. **Point-Slope Form: \( y - y_1 = m(x - x_1) \)**
- The point-slope form equation is given using a point (1, 2):
```
y - 2 = -2(x - 1)
```
- This form emphasizes the slope (m = -2) and a specific point on the line.
3. **Standard Form: \( Ax + By = C \)**
- The standard form equation is expressed as:
```
2x + y = 4
```
- This format rearranges the linear equation into a standardized algebraic form where A, B, and C are integers.
**Note:** Each form is a valid representation of the same line on the graph, showcasing different approaches to expressing linear equations.
Expert Solution
Step 1
To find:-
Slope intercept form, point slope form and standard equation of line from given graph
Step by step
Solved in 5 steps with 2 images
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