the graph, derive the equation of the line in slope-intercept form.

Question

y=−3x−4
y=3x+4
3x−y=4
y=3x−4

Answer 1

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!

Answer 2

What is the answer?

Answer 3

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!