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 \( y = mx + b \) form, we can rewrite the equations in this format if they aren't already. The \( y = mx + b \) form describes a linear equation where \( m \) is the slope and \( b \) is the y-intercept.

Now, let's analyze each equation:

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 already in the form \( y = mx + b \) where \( m = -2 \) and \( b = 3 \).

3. **y = 3x + 1**
- This is already in the form \( y = mx + b \) where \( m = 3 \) and \( b = 1 \).

4. **2y = 6x + 2**
- Divide everything by 2 to get \( y = 3x + 1 \). Now it is in the form \( y = mx + b \).

5. **y - 5x = 2**
- Rearranging gives \( y = 5x + 2 \), which is in the form \( y = mx + b \).

6. **y - 4x + 1 = 0**
- Rearranging gives \( y = 4x - 1 \), which is in the form \( y = mx + b \).

### Summary:
All of the equations provided can be expressed in \( y = mx + b \) form. Therefore, the correct options that are already in this form are:

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

All options are ultimately expressible in slope-intercept form (y = mx + b).