To determine which equations are in the \( y = mx + b \) form (slope-intercept form), we can check each equation:
- \( y = 5x - 4 \) (This is already in \( y = mx + b \) form.)
- \( y = -2x + 3 \) (This is already in \( y = mx + b \) form.)
- \( y = 3x + 1 \) (This is already in \( y = mx + b \) form.)
- \( 2y = 6x + 2 \) (Dividing the entire equation by 2 gives: \( y = 3x + 1 \); thus, it can be converted to the form.)
- \( y - 5x = 2 \) (Rearranging gives \( y = 5x + 2 \); thus, it can be converted to the form.)
- \( y - 4x + 1 = 0 \) (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).