Asked by Kadyn

the graph, derive the equation of the line in slope-intercept form.
y=−3x−4
y=3x+4
3x−y=4
y=3x−4
Answered by Kadyn
What is the answer?
Answered by GPT-4o mini
To derive the equation of a line in slope-intercept form (\(y = mx + b\)), we need to identify the slope (\(m\)) and the y-intercept (\(b\)) from the given options. Let's analyze each of the provided equations:

1. **\(y = -3x - 4\)**
- This is already in slope-intercept form: \(m = -3\), \(b = -4\).

2. **\(y = 3x + 4\)**
- This is also in slope-intercept form: \(m = 3\), \(b = 4\).

3. **\(3x - y = 4\)**
- To convert this to slope-intercept form, solve for \(y\):
\[
-y = -3x + 4 \quad \Rightarrow \quad y = 3x - 4
\]
- Now it is in slope-intercept form: \(m = 3\), \(b = -4\).

4. **\(y = 3x - 4\)**
- This is already in slope-intercept form: \(m = 3\), \(b = -4\).

### Summary of the equations:
- **\(y = -3x - 4\)**: Slope = -3, y-intercept = -4
- **\(y = 3x + 4\)**: Slope = 3, y-intercept = 4
- **\(3x - y = 4\)**: Converts to \(y = 3x - 4\): Slope = 3, y-intercept = -4
- **\(y = 3x - 4\)**: Slope = 3, y-intercept = -4

If you have a specific equation you want to derive or analyze further, please let me know!
Answered by GPT-4o mini
The question seems to ask for the equations of the lines provided, expressed in slope-intercept form. All four equations you provided can be derived or are already in slope-intercept form. Here's the summary of the results:

1. **\(y = -3x - 4\)**: This is already in slope-intercept form.

2. **\(y = 3x + 4\)**: This is also already in slope-intercept form.

3. **\(3x - y = 4\)**: When converted to slope-intercept form, it becomes:
\[
y = 3x - 4
\]

4. **\(y = 3x - 4\)**: This is also already in slope-intercept form.

### Summary of Slope-Intercept Forms:
- **1**: \(y = -3x - 4\) (Slope = -3, Intercept = -4)
- **2**: \(y = 3x + 4\) (Slope = 3, Intercept = 4)
- **3**: \(y = 3x - 4\) (Slope = 3, Intercept = -4)
- **4**: \(y = 3x - 4\) (Again, same as ^3)

If you are looking for one specific answer or specific details on what you need to derive, please clarify!