Which equations are already in y=mx+b form?

Question

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3 points
Captionless Image
Option 1
Option 2
Option 3
Option 4
Option 5
Option 6

Answer 1

To determine which equations are already in the slope-intercept form \(y = mx + b\), we need to identify the equations that have been rearranged such that \(y\) is isolated on one side of the equation, with \(m\) being the slope and \(b\) being the y-intercept.

Without the specific equations visible, I can't provide the exact answers. However, I can guide you on how to recognize if an equation is in the proper form:

1. Look for the variable \(y\) on the left side of the equation.
2. Ensure that the equation takes the form \(y = mx + b\), where:
   • \(m\) represents the slope (a coefficient of \(x\)).
   • \(b\) represents the y-intercept (a constant).

Common rearrangements to find this form include:

• Adding or subtracting terms on both sides of the equation.
• Dividing or multiplying to isolate \(y\).

If you can provide the specific equations or options, I can help determine which ones are correctly in the \(y = mx + b\) form.

Answer 2

Captionless Image

Answer 3

It seems there may have been an attempt to share an image or additional content, but as a text-based AI, I'm unable to see images or captions. However, if you can type out the equations or options presented in that image, I’d be glad to help you determine which ones are in the \(y = mx + b\) form.

Please share the equations, and I'll provide the needed assistance!

Answer 4

1. y=5x-4
2. y=-2x+3
3.y=3x+1
4. 2y=6x+2
5. y-5x=2
6. y-4x+1=0

Answer 5

Let's analyze each equation to see which ones are in the slope-intercept form \(y = mx + b\):

1. \(y = 5x - 4\)

   • This is already in the form \(y = mx + b\) where \(m = 5\) and \(b = -4\).

2. \(y = -2x + 3\)

   • This is also in the form \(y = mx + b\) where \(m = -2\) and \(b = 3\).

3. \(y = 3x + 1\)

   • This is in the form \(y = mx + b\) where \(m = 3\) and \(b = 1\).

4. \(2y = 6x + 2\)

   • To put this in the correct form, divide by 2: \[ y = 3x + 1 \]
   • This is now in the form \(y = mx + b\) where \(m = 3\) and \(b = 1\).

5. \(y - 5x = 2\)

   • Rearranging gives: \[ y = 5x + 2 \]
   • This is in the form \(y = mx + b\) where \(m = 5\) and \(b = 2\).

6. \(y - 4x + 1 = 0\)

   • Rearranging gives: \[ y = 4x - 1 \]
   • This is in the form \(y = mx + b\) where \(m = 4\) and \(b = -1\).

Summary:

The following equations are already in \(y = mx + b\) form:

1. \(y = 5x - 4\)
2. \(y = -2x + 3\)
3. \(y = 3x + 1\)
4. \(2y = 6x + 2\) (after simplification)
5. \(y - 5x = 2\) (after rearranging)
6. \(y - 4x + 1 = 0\) (after rearranging)

So all options listed (1 through 6) can ultimately be expressed in the slope-intercept form.

Answer 6

Which equations are already in y=mx+b form?

Answer 7

Let's identify which of the provided equations are already in the slope-intercept form \(y = mx + b\) without any modification required.

Here are the equations again:

1. \(y = 5x - 4\)

   • This is already in the \(y = mx + b\) form.

2. \(y = -2x + 3\)

   • This is already in the \(y = mx + b\) form.

3. \(y = 3x + 1\)

   • This is already in the \(y = mx + b\) form.

4. \(2y = 6x + 2\)

   • This needs to be simplified. Dividing everything by 2 gives: \[ y = 3x + 1 \]
   • So, after simplification, this is in the \(y = mx + b\) form, but it's not in that form yet.

5. \(y - 5x = 2\)

   • Rearranging gives: \[ y = 5x + 2 \]
   • So, this is also in \(y = mx + b\) after rearranging.

6. \(y - 4x + 1 = 0\)

   • Rearranging gives: \[ y = 4x - 1 \]
   • So, this is also in the \(y = mx + b\) form after rearranging.

Conclusion:

The equations that are already in the \(y = mx + b\) form (without any modification) are:

• 1. \(y = 5x - 4\)
• 2. \(y = -2x + 3\)
• 3. \(y = 3x + 1\)

Equations 4, 5, and 6 require some manipulation to reach that form.