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:
- y = 5x - 4 - This is already in the correct form (slope = 5, y-intercept = -4).
- y = -2x + 3 - This is also in the correct form (slope = -2, y-intercept = 3).
- y = 3x + 1 - This is in the correct form (slope = 3, y-intercept = 1).
- 2y = 6x + 2 - To rewrite this, divide everything by 2:
\( y = 3x + 1 \). This is now in the correct form. - y - 5x = 2 - Rearranging gives us \( y = 5x + 2 \). This is in the correct form.
- 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 \( y = mx + b \):
- \( y = 5x - 4 \) (in form)
- \( y = -2x + 3 \) (in form)
- \( y = 3x + 1 \) (in form)
- \( y = 3x + 1 \) (in form after rearranging)
- \( y = 5x + 2 \) (in form after rearranging)
- \( y = 4x - 1 \) (in form after rearranging)
In conclusion, all six equations can be or are already in \( y = mx + b \) form.