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Which equations are already in y=mx+b form? [Hint you will be using these same 6 equations for the entire portfolio.- so go ahead and change all equations to the correct form.]

= 65
1. y = 57 - 4
2. y = -2x + 3
3. y = 3x+1
4. 2y = 6x + 2
5. у - 5х = 2
6. у - 4г + 1 = 0

Option 1

• Option 2

Option 3

Option 4

Option 5
Option 6

9 answers

To determine which equations are already in the \(y = mx + b\) form, we need to convert all the given equations to this format.

Here’s the given list along with the transformations for each equation:

  1. Equation: \(y = 57 - 4\)

    • Simplified: \(y = 53\)
    • Form: \(y = 0x + 53\) (This is in \(y = mx + b\) form)

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

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

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

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

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

    • Rearranging: Divide everything by 2:
    • Result: \(y = 3x + 1\)
    • Form: This is in \(y = mx + b\) form.

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

    • Rearranging: Add \(5x\) to both sides:
    • Result: \(y = 5x + 2\)
    • Form: This is in \(y = mx + b\) form.

  6. Equation: \(y - 4g + 1 = 0\)

    • Rearranging: Add \(4g - 1\) to both sides:
    • Result: \(y = 4g - 1\)
    • Form: This is not strictly in \(y = mx + b\) form as there is a "g" variable.

Summary of Results:

  • Equations already in \(y = mx + b\) form:

      1. \(y = -2x + 3\)
      1. \(y = 3x + 1\)
      1. \(y = 3x + 1\) (from the original)
      1. \(y = 5x + 2\)
      1. \(y = 53\) (in the general linear form, where \(m = 0\))

  • Not in the correct form:

      1. \(y = 4g - 1\)

Finalized Equations:

  1. \(y = 53\) (or \(y = 0x + 53\))
  2. \(y = -2x + 3\)
  3. \(y = 3x + 1\)
  4. \(y = 3x + 1\) (simplified)
  5. \(y = 5x + 2\)
  6. \(y = 4g - 1\) (not \(y = mx + b\))

Thus, the equations in \(y = mx + b\) form are 1, 2, 3, 4, and 5 (with 6 being excluded due to having a different variable).

Answer

Here are the equations that are already in the \(y = mx + b\) form:

  1. \(y = 53\) (this can be considered as \(y = 0x + 53\))
  2. \(y = -2x + 3\)
  3. \(y = 3x + 1\)
  4. \(y = 3x + 1\) (from \(2y = 6x + 2\))
  5. \(y = 5x + 2\)

The only equation that is not in the \(y = mx + b\) form is:

  1. \(y = 4g - 1\) (this contains a variable \(g\) instead of \(x\))

Summary:

  • In \(y = mx + b\) form: 1, 2, 3, 4, 5
  • Not in \(y = mx + b\) form: 6

If you need the full forms of each equation or any additional information, let me know!

Only the answer

Equations in \(y = mx + b\) form: 1, 2, 3, 4, 5.
Not in \(y = mx + b\) form: 6.

What option?

Here are the options based on your earlier request:

  • Option 1: \(y = 53\)
  • Option 2: \(y = -2x + 3\)
  • Option 3: \(y = 3x + 1\)
  • Option 4: \(y = 3x + 1\) (from \(2y = 6x + 2\))
  • Option 5: \(y = 5x + 2\)
  • Option 6: \(y = 4g - 1\)

Equations already in \(y = mx + b\) form: Option 2, Option 3, Option 4, Option 5.

Option 1 is also a valid linear equation, implying \(m = 0\).

Option 6 is not in the correct form.

Only right answer I don’t care about the wrong answers

Options in \(y = mx + b\) form: 2, 3, 4, 5.