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:
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y = 5x - 4
- This is already in the form \( y = mx + b \) where \( m = 5 \) and \( b = -4 \).
-
y = -2x + 3
- This is already in the form \( y = mx + b \) where \( m = -2 \) and \( b = 3 \).
-
y = 3x + 1
- This is already in the form \( y = mx + b \) where \( m = 3 \) and \( b = 1 \).
-
2y = 6x + 2
- Divide everything by 2 to get \( y = 3x + 1 \). Now it is in the form \( y = mx + b \).
-
y - 5x = 2
- Rearranging gives \( y = 5x + 2 \), which is in the form \( y = mx + b \).
-
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:
- \( y = 5x - 4 \)
- \( y = -2x + 3 \)
- \( y = 3x + 1 \)
- \( 2y = 6x + 2 \) (after rearranging, it becomes \( y = 3x + 1 \))
- \( y - 5x = 2 \) (after rearranging, it becomes \( y = 5x + 2 \))
- \( y - 4x + 1 = 0 \) (after rearranging, it becomes \( y = 4x - 1 \))
All options are ultimately expressible in slope-intercept form (y = mx + b).