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write each equation in standard form. y-3=2(x+4)

A. -2x+y=5
B.-2x+y=11
C.2x-y=-11
D.2x+y=11

1 answer

To write the equation \( y - 3 = 2(x + 4) \) in standard form, we will first simplify it and then rearrange it.

  1. Distribute on the right side: \[ y - 3 = 2x + 8 \]

  2. Add 3 to both sides: \[ y = 2x + 11 \]

  3. Now, we want to rearrange this into standard form \( Ax + By = C \). We will move \( 2x \) to the left: \[ -2x + y = 11 \]

  4. To present the equation in the standard form with a positive \( x \) coefficient, we can multiply through by -1: \[ 2x - y = -11 \]

Now, rearranging gives: \[ 2x - y = -11 \] If we want to match it with the options provided, we rewrite it as: \[ 2x + (-y) = -11 \]

Now we can see that:

The solution choices presented were: A. \(-2x + y = 5\) B. \(-2x + y = 11\) C. \(2x - y = -11\) D. \(2x + y = 11\)

The correct answer is: C. \(2x - y = -11\)