Question

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

Answer 1

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.