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

Question

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 in the \( y = mx + b \) form (slope-intercept form), we can check each equation:

1. \( y = 5x - 4 \) (This is already in \( y = mx + b \) form.)
2. \( y = -2x + 3 \) (This is already in \( y = mx + b \) form.)
3. \( y = 3x + 1 \) (This is already in \( y = mx + b \) form.)
4. \( 2y = 6x + 2 \) (Dividing the entire equation by 2 gives: \( y = 3x + 1 \); thus, it can be converted to the form.)
5. \( y - 5x = 2 \) (Rearranging gives \( y = 5x + 2 \); thus, it can be converted to the form.)
6. \( y - 4x + 1 = 0 \) (Rearranging gives \( y = 4x - 1 \); thus, it can be converted to the form.)

Now, let’s summarize the results:

• Already in \( y = mx + b \) form:

  • 1: \( y = 5x - 4 \)
  • 2: \( y = -2x + 3 \)
  • 3: \( y = 3x + 1 \)

• Can be converted to \( y = mx + b \) form:

  • 4: \( 2y = 6x + 2 \)
  • 5: \( y - 5x = 2 \)
  • 6: \( y - 4x + 1 = 0 \)

Final Answer of those already in \( y = mx + b \) form:

• Equations 1, 2, and 3 (Options 1, 2, and 3).