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 $y$: $$-y=-3x+4\Rightarrow y=3x-4$$
   • 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!