Which equations are in standard form

Which equations are in standard form? Check all that apply y = 2x + 5 2x + 3y = –6 –4x + 3y = 12 y = y equals StartFraction 3 Over 2 EndFraction x minus 9.x – 9 StartFraction one-half EndFraction x plus 3 equals 6.x + 3 = 6 x – y = 5 5x + 3y = 5 x plus 3 y equals StartFraction one-half EndFraction.

The Correct Answer and Explanation is :

To determine which equations are in standard form, we need to recognize the general form of the equation of a line in two variables, which is:

[
Ax + By = C
]

Where:

• ( A ) and ( B ) are integers (with ( A ) being nonzero),
• ( x ) and ( y ) are variables,
• ( C ) is a constant.

The equation should have all variables on one side, and the coefficients of ( x ) and ( y ) should be integers.

Let’s go through the equations one by one and check if they are in standard form:

1. ( y = 2x + 5 )
   This equation is not in standard form because it is written in slope-intercept form ( y = mx + b ). To put it in standard form, subtract ( 2x ) from both sides:
   [
   -2x + y = 5
   ]
   This would be in standard form.
2. ( 2x + 3y = -6 )
   This equation is in standard form. It has the format ( Ax + By = C ), with ( A = 2 ), ( B = 3 ), and ( C = -6 ).
3. ( -4x + 3y = 12 )
   This equation is in standard form. It has ( A = -4 ), ( B = 3 ), and ( C = 12 ).
4. ( y = \frac{3}{2}x – 9 )
   This equation is in slope-intercept form. To put it into standard form, multiply through by 2 to eliminate the fraction:
   [
   2y = 3x – 18
   ]
   Then, subtract ( 3x ) from both sides to get:
   [
   -3x + 2y = -18
   ]
   Now, it is in standard form.
5. ( \frac{1}{2}x + 3 = 6 )
   This equation is not in standard form. First, subtract 3 from both sides:
   [
   \frac{1}{2}x = 3
   ]
   Then multiply through by 2 to eliminate the fraction:
   [
   x = 6
   ]
   This is not in standard form.
6. ( x – y = 5 )
   This equation is in standard form. It has ( A = 1 ), ( B = -1 ), and ( C = 5 ).
7. ( 5x + 3y = 5 )
   This equation is in standard form. It is already in the correct form ( Ax + By = C ), with ( A = 5 ), ( B = 3 ), and ( C = 5 ).
8. ( x + 3y = \frac{1}{2} )
   This equation is not in standard form because of the fraction on the right side. To convert to standard form, multiply through by 2:
   [
   2x + 6y = 1
   ]
   Now, it is in standard form.

Summary of equations in standard form:

• ( 2x + 3y = -6 )
• ( -4x + 3y = 12 )
• ( -3x + 2y = -18 ) (from the equation ( y = \frac{3}{2}x – 9 ))
• ( x – y = 5 )
• ( 5x + 3y = 5 )
• ( 2x + 6y = 1 ) (from the equation ( x + 3y = \frac{1}{2} ))

These are the equations that are in standard form.