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Which equations are already in y=mx+b form? * 3 points

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
Option 1
Option 2
Option 3
Option 4
Option 5
Option 6

1 answer

To determine which equations are already in the \( y = mx + b \) form (where \( m \) is the slope and \( b \) is the y-intercept), we can analyze each of the provided equations:

  1. y = 5x - 4 - This is already in the correct form (slope = 5, y-intercept = -4).
  2. y = -2x + 3 - This is also in the correct form (slope = -2, y-intercept = 3).
  3. y = 3x + 1 - This is in the correct form (slope = 3, y-intercept = 1).
  4. 2y = 6x + 2 - To rewrite this, divide everything by 2:
    \( y = 3x + 1 \). This is now in the correct form.
  5. y - 5x = 2 - Rearranging gives us \( y = 5x + 2 \). This is in the correct form.
  6. y - 4x + 1 = 0 - Rearranging gives us \( y = 4x - 1 \). This is in the correct form.

So, all of the options can be put into the slope-intercept form \( y = mx + b \):

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

In conclusion, all six equations can be or are already in \( y = mx + b \) form.